Advertisements
Advertisements
प्रश्न
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
पर्याय
(– 1, ∞)
(– 2, – 1)
(– ∞, – 2)
[– 1, 1]
Advertisements
उत्तर
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is (– 2, – 1).
Explanation:
Given,
f(x) = 2x3 + 9x2 + 12x – 1
f'(x) = 6x2 + 18x + 12 = 6(x2 + 3x + 2)
For increasing or decreasing, f'(x) = a
x2 + 3x + 2 = 0
`\implies` x = – 1, – 2
Sign scheme indicates
So the function is decreasing in (– 2, – 1).
APPEARS IN
संबंधित प्रश्न
Find the value of c in Rolle's theorem for the function `f(x) = x^3 - 3x " in " (-sqrt3, 0)`
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
- strictly decreasing
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
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) = x2 − x sin x is an increasing function on (0, π/2) ?
Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is
The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if
The function f(x) = x9 + 3x7 + 64 is increasing on
Show that the function f given by f(x) = tan–1 (sin x + cos x) is decreasing for all \[x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) .\]
Find the intervals in which the function \[f(x) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] is
(a) strictly increasing
(b) strictly decreasing
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.
Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x2 – x3, x ∈ R.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Test whether the following function is increasing or decreasing.
f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0
Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
The interval on which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
The function f (x) = x2, for all real x, is ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.
Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
