Advertisements
Advertisements
प्रश्न
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
Advertisements
उत्तर
f(x) =`("x - 2")/("x + 1")`, x ≠ 0
For function to be increasing, f '(x) > 0
Then f '(x) = `(("x + 1") "d"/"dx" ("x - 2") - ("x - 2") "d"/"dx" ("x" + 1))/("x + 1")^2`
`= (("x + 1") - ("x - 2"))/("x + 1")^2 = ("x" + 1 - "x" + 2)/("x" + 1)^2`
`= 3/("x + 1")^2` > 0 ....[∵ (x + 1) ≠ 0, (x + 1)2 > 0]
Thus, f(x) is an increasing function for x ≠ - 1.
APPEARS IN
संबंधित प्रश्न
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 + 9x2 + 12x + 20 ?
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 \[f\left( x \right) = \frac{3}{10} x^4 - \frac{4}{5} x^3 - 3 x^2 + \frac{36}{5}x + 11\] ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \left\{ x(x - 2) \right\}^2\] ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
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) ?
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
If the function f(x) = 2 tan x + (2a + 1) loge | sec x | + (a − 2) x is increasing on R, then
If the function f(x) = x3 − 9kx2 + 27x + 30 is increasing on R, then
The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.
Find `dy/dx,if e^x+e^y=e^(x-y)`
Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find the inverse of f: N → S, where S is range of f.
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 function f(x) = x3 + 6x2 + 12x − 5 is increasing or decreasing for all x ∈ R
Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing
If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______
State whether the following statement is True or False:
If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
The function f(x) = sin x + 2x is ______
Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
The function f(x) = tan-1 x is ____________.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:
If f(x) = x3 + 4x2 + λx + 1(λ ∈ R) is a monotonically decreasing function of x in the largest possible interval `(–2, (–2)/3)` then ______.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
If f(x) = x + cosx – a then ______.
