Advertisements
Advertisements
Question
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
Options
(– 1, ∞)
(– 2, – 1)
(– ∞, – 2)
[– 1, 1]
Advertisements
Solution
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
RELATED QUESTIONS
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
Which of the following functions are strictly decreasing on `(0, pi/2)`?
- cos x
- cos 2x
- cos 3x
- tan x
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Without using the derivative show that the function f (x) = 7x − 3 is strictly increasing function on R ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?
Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?
Show that the function f given by f(x) = 10x is increasing for all x ?
What are the values of 'a' for which f(x) = ax is decreasing on R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval
Let ϕ(x) = f(x) + f(2a − x) and f"(x) > 0 for all x ∈ [0, a]. Then, ϕ (x)
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
Find `dy/dx,if e^x+e^y=e^(x-y)`
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
State whether the following statement is True or False:
The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
The function `1/(1 + x^2)` is increasing in the interval ______
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
The function f(x) = tanx – x ______.
The function f(x) = x2 – 2x is increasing in the interval ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
The function `"f"("x") = "log" (1 + "x") - (2"x")/(2 + "x")` is increasing on ____________.
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is
Find the value of x for which the function f(x)= 2x3 – 9x2 + 12x + 2 is decreasing.
Given f(x) = 2x3 – 9x2 + 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`
Function f(x) = x100 + sinx – 1 is increasing for all x ∈ ______.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
