Advertisements
Advertisements
प्रश्न
y = x(x – 3)2 decreases for the values of x given by : ______.
विकल्प
1 < x < 3
x < 0
x > 0
`0 < x < 3/2`
Advertisements
उत्तर
y = x(x – 3)2 decreases for the values of x given by : 1 < x < 3.
Explanation:
Here y = x(x – 3)2
`"dy"/"dx" = x * 2(x - 3) + (x - 3)^2 * 1`
⇒ `"dy"/"dx" = 2x(x - 3) + (x - 3)^2`
For increasing and decreasing `"dy"/"dx"` = 0
∴ 2x(x – 3) + (x – 3)2 = 0
⇒ (x – 3)(2x + x – 3) = 0
⇒ (x – 3)(3x – 3) = 0
⇒ 3(x – 3)(x – 1) = 0
∴ x = 1, 3
∴ Possible intervals are `(– oo, 1), (1, 3), (3, oo)`
`"dy"/"dx"` = (x – 3)(x – 1)
For `(– oo, 1)` = (–) (–) = (+) increasing
For (1, 3) = (–) (+) = (–) decreasing
For `(3, oo)` = (+) (+) = (+) increasing
So the function decreases in (1, 3) or 1 < x < 3
APPEARS IN
संबंधित प्रश्न
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 ?
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
(x + 1)3 (x − 3)3
Find the values of x for `y = [x(x - 2)]^2` is an increasing function.
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Find the interval in which the following function are increasing or decreasing f(x) = 5x3 − 15x2 − 120x + 3 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 15x2 + 36x + 1 ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
The function \[f\left( x \right) = \frac{x}{1 + \left| x \right|}\] is
Function f(x) = ax is increasing on R, if
Let ϕ(x) = f(x) + f(2a − x) and f"(x) > 0 for all x ∈ [0, a]. Then, ϕ (x)
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).
Find MPC ( Marginal propensity to Consume ) and APC ( Average Propensity to Consume ) if the expenditure Ec of a person with income I is given as Ec = ( 0.0003 ) I2 + ( 0.075 ) I when I = 1000.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly decreasing
The slope of tangent at any point (a, b) is also called as ______.
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
The values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.
If f(x) = x3 – 15x2 + 84x – 17, then ______.
The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
The function `"f"("x") = "log" (1 + "x") - (2"x")/(2 + "x")` is increasing on ____________.
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
If f(x) = x + cosx – a then ______.
A function f is said to be increasing at a point c if ______.
Which form shows that \[f'(x)=3x^2-6x+4\] is positive for every \[x\in\mathbf{R}\]?
For \[f(x)=4x^3-6x^2-72x+30\], which factorization of \[f'(x)\] is correct?
