###### Advertisements

###### Advertisements

If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______

###### Advertisements

#### Solution

If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ **R - {0}**

#### RELATED QUESTIONS

Price P for demand D is given as P = 183 +120D - 3D^{2} Find D for which the price is increasing

The amount of pollution content added in air in a city due to *x*-diesel vehicles is given by P(*x*) = 0.005*x*^{3} + 0.02*x*^{2} + 30*x*. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.

**Test whether the function is increasing or decreasing.**

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,

The function f (x) = x^{3} – 3x^{2} + 3x – 100, x∈ R is _______.

(A) increasing

(B) decreasing

(C) increasing and decreasing

(D) neither increasing nor decreasing

Show that the function given by f(x) = 3x + 17 is strictly increasing on **R**.

Which of the following functions are strictly decreasing on `(0, pi/2)`?

- cos x
- cos 2x
- cos 3x
- tan x

Let I be any interval disjoint from (−1, 1). Prove that the function f given by `f(x) = x + 1/x` is strictly increasing on I.

The interval in which y = x^{2} e^{–x} is increasing is ______.

Water is dripping out from a conical funnel of semi-verticle angle `pi/4` at the uniform rate of `2 cm^2/sec`in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is 4 cm, find the rate of decrease of the slant height of the water.

Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R ?

Show that f(x) = \[\frac{1}{1 + x^2}\] is neither increasing nor decreasing on R ?

Find the interval in which the following function are increasing or decreasing f(x) = 6 − 9x − x^{2 }?

Find the interval in which the following function are increasing or decreasing f(x) = 8 + 36x + 3x^{2} − 2x^{3 }?

Find the interval in which the following function are increasing or decreasing f(x) = 2x^{3} − 15x^{2} + 36x + 1 ?

Find the interval in which the following function are increasing or decreasing f(x) = −2x^{3} − 9x^{2} − 12x + 1 ?

Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)^{2 }?

Find the interval in which the following function are increasing or decreasing f(x) = 2x^{3} − 24x + 7 ?

Find the interval in which the following function are increasing or decreasing f(x) = x^{8} + 6x^{2 }?

Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?

Prove that the function f(x) = x^{3} − 6x^{2} + 12x − 18 is increasing on R ?

Find the intervals in which f(x) = (x + 2) e^{−x} is increasing or decreasing ?

Prove that the function f given by f(x) = log cos x is strictly increasing on (−π/2, 0) and strictly decreasing on (0, π/2) ?

Show that f(x) = x^{2} − x sin x is an increasing function on (0, π/2) ?

Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?

Find the interval in which f(x) is increasing or decreasing f(x) = sinx(1 + cosx), 0 < x < \[\frac{\pi}{2}\] ?

Write the set of values of 'a' for which f(x) = log_{a} x is decreasing in its domain ?

If g (x) is a decreasing function on R and f(x) = tan^{−1} [g (x)]. State whether f(x) is increasing or decreasing on R ?

Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?

Let f(x) = x^{3}^{ }+ ax^{2} + bx + 5 sin^{2}x be an increasing function on the set R. Then, a and b satisfy

Function *f*(*x*) = cos *x* − 2 λ *x* is monotonic decreasing when

Function f(x) = x^{3} − 27x + 5 is monotonically increasing when

Function f(x) = | x | − | x − 1 | is monotonically increasing when

If the function *f*(*x*) = cos |*x*| − 2*ax* + *b* increases along the entire number scale, then

If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`

Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R.

For manufacturing x units, labour cost is 150 – 54x and processing cost is x^{2}. Price of each unit is p = 10800 – 4x^{2}. Find the value of x for which Total cost is decreasing.

The total cost of manufacturing x articles is C = 47x + 300x^{2} − x^{4}. Find x, for which average cost is increasing.

The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.

Test whether the following functions are increasing or decreasing : f(x) = x^{3} – 6x^{2} + 12x – 16, x ∈ R.

Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x^{2} – x^{3}, x ∈ R.

Test whether the following functions are increasing or decreasing : f(x) = `(1)/x`, x ∈ R , x ≠ 0.

Find the values of x for which the following functions are strictly increasing : f(x) = 2x^{3} – 3x^{2} – 12x + 6

Find the values of x for which the following functions are strictly increasing : f(x) = 3 + 3x – 3x^{2} + x^{3}

Find the values of x for which the following func- tions are strictly increasing : f(x) = x^{3} – 6x^{2} – 36x + 7

**Find the values of x for which the following functions are strictly decreasing:**

f(x) = 2x^{3} – 3x^{2} – 12x + 6

Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`

Find the values of x for which the following functions are strictly decreasing : f(x) = x^{3} – 9x^{2} + 24x + 12

Find the values of x for which the function f(x) = x^{3} – 12x^{2} – 144x + 13 (a) increasing (b) decreasing

Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.

show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.

Show that f(x) = x – cos x is increasing for all x.

Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.

Prove that y = `(4sinθ)/(2 + cosθ) - θ` is an increasing function if `θ ∈[0, pi/2]`

**Choose the correct option from the given alternatives :**

Let f(x) = x^{3} – 6x^{2} + 9x + 18, then f(x) is strictly decreasing in ______.

Solve the following : Find the intervals on which the function y = x^{x}, (x > 0) is increasing and decreasing.

**Solve the following: **

Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.

**Test whether the following function is increasing or decreasing.**

f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0

**Find the value of x, such that f(x) is increasing function.**

f(x) = 2x^{3} - 15x^{2} - 144x - 7

**Find the value of x, such that f(x) is decreasing function.**

f(x) = 2x^{3} – 15x^{2} – 84x – 7

**Find the value of x such that f(x) is decreasing function.**

f(x) = x^{4} − 2x^{3} + 1

For manufacturing x units, labour cost is 150 – 54x and processing cost is x^{2}. Price of each unit is p = 10800 – 4x^{2}. Find the values of x for which Revenue is increasing.

**Choose the correct alternative.**

The function f(x) = x^{3} - 3x^{2} + 3x - 100, x ∈ R is

Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.

Let f(x) = x^{3} − 6x^{2} + 9𝑥 + 18, then f(x) is strictly decreasing in ______

Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function

Show that f(x) = x – cos x is increasing for all x.

Show that the function f(x) = x^{3} + 10x + 7 for x ∈ R is strictly increasing

Test whether the function f(x) = x^{3} + 6x^{2} + 12x − 5 is increasing or decreasing for all x ∈ R

Test whether the following function f(x) = 2 – 3x + 3x^{2} – x^{3}, x ∈ R is increasing or decreasing

Find the values of x for which the function f(x) = 2x^{3} – 6x^{2} + 6x + 24 is strictly increasing

Find the values of x for which the function f(x) = x^{3} – 6x^{2} – 36x + 7 is strictly increasing

Find the values of x, for which the function f(x) = x^{3} + 12x^{2} + 36𝑥 + 6 is monotonically decreasing

Find the values of x for which f(x) = 2x^{3} – 15x^{2} – 144x – 7 is

**(a)** Strictly increasing**(b)** strictly decreasing

**Choose the correct alternative:**

The function f(x) = x^{3} – 3x^{2} + 3x – 100, x ∈ R is

The price P for the demand D is given as P = 183 + 120D − 3D^{2}, then the value of D for which price is increasing, is ______.

The slope of tangent at any point (a, b) is also called as ______.

The total cost function for production of articles is given as C = 100 + 600x – 3x^{2}, then the values of x for which the total cost is decreasing is ______

**State whether the following statement is True or False:**

The function f(x) = `3/x` + 10, x ≠ 0 is decreasing

The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing

**State whether the following statement is True or False: **

If the function f(x) = x^{2} + 2x – 5 is an increasing function, then x < – 1

Find the values of x such that f(x) = 2x^{3} – 15x^{2} + 36x + 1 is increasing function

Find the values of x such that f(x) = 2x^{3} – 15x^{2} – 144x – 7 is decreasing function

Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing

By completing the following activity, find the values of x such that f(x) = 2x^{3} – 15x^{2} – 84x – 7 is decreasing function.

**Solution: **f(x) = 2x^{3} – 15x^{2} – 84x – 7

∴ f'(x) = `square`

∴ f'(x) = 6`(square) (square)`

Since f(x) is decreasing function.

∴ f'(x) < 0

**Case 1:** `(square)` > 0 and (x + 2) < 0

∴ x ∈ `square`

**Case 2:** `(square)` < 0 and (x + 2) > 0

∴ x ∈ `square`

∴ f(x) is decreasing function if and only if x ∈ `square`

A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is

The function f(x) = 9 - x^{5} - x^{7} is decreasing for

The area of the square increases at the rate of 0.5 cm^{2}/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.

A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______

f(x) = `{{:(0"," x = 0 ), (x - 3"," x > 0):}` The function f(x) is ______

The function f(x) = sin x + 2x is ______

The values of k for which the function f(x) = kx^{3} – 6x^{2} + 12x + 11 may be increasing on R are ______.

The function `1/(1 + x^2)` is increasing in the interval ______

If f(x) = x^{3} – 15x^{2} + 84x – 17, then ______.

Show that f(x) = 2x + cot^{–1}x + `log(sqrt(1 + x^2) - x)` is increasing in R

Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.

Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.

In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.

The function f: N → N, where

f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is

Which of the following graph represent the strictly increasing function.

Let x_{0} be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x_{0} – h, ro + h) containing x_{0}. Then which of the following statement is/ are true for the above statement.

Function given by f(x) = sin x is strictly increasing in.

Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.

The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is

Show that function f(x) = tan x is increasing in `(0, π/2)`.

State whether the following statement is true or false.

If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).

If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.

Find the value of x for which the function f(x)= 2x^{3} – 9x^{2} + 12x + 2 is decreasing.

Given f(x) = 2x^{3} – 9x^{2 }+ 12x + 2

∴ f'(x) = `squarex^2 - square + square`

∴ f'(x) = `6(x - 1)(square)`

Now f'(x) < 0

∴ 6(x – 1)(x – 2) < 0

Since ab < 0 ⇔a < 0 and b < 0 or a > 0 and b < 0

**Case 1: **(x – 1) < 0 and (x – 2) < 0

∴ x < `square` and x > `square`

Which is contradiction

**Case 2:** x – 1 and x – 2 < 0

∴ x > `square` and x < `square`

1 < `square` < 2

f(x) is decreasing if and only if x ∈ `square`

Let 'a' be a real number such that the function f(x) = ax^{2} + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax^{2} – 6x + 15, x∈R has a ______.

Let f(x) be a function such that; f'(x) = log_{1/3}(log_{3}(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.

Let f(x) = tan^{–1}`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.

The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.

If f(x) = x + cosx – a then ______.

Function f(x) = `log(1 + x) - (2x)/(2 + x)` is monotonically increasing when ______.

y = log x satisfies for x > 1, the inequality ______.

Function f(x) = x^{100} + sinx – 1 is increasing for all x ∈ ______.

Let f : R `rightarrow` R be a positive increasing function with `lim_(x rightarrow ∞) (f(3x))/(f(x))` = 1 then `lim_(x rightarrow ∞) (f(2x))/(f(x))` = ______.

Let f(x) = `x/sqrt(a^2 + x^2) - (d - x)/sqrt(b^2 + (d - x)^2), x ∈ R` where a, b and d are non-zero real constants. Then ______.

The interval in which the function f(x) = `(4x^2 + 1)/x` is decreasing is ______.

A function f is said to be increasing at a point c if ______.

The function f(x) = x^{3} + 3x is increasing in interval ______.

Find the interval/s in which the function f : R `rightarrow` R defined by f(x) = xe^{x}, is increasing.

The function f(x) = sin^{4}x + cos^{4}x is an increasing function if ______.

The intevral in which the function f(x) = 5 + 36x – 3x^{2} increases will be ______.