Advertisements
Advertisements
प्रश्न
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
विकल्प
(– 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
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
Find the intervals in which the following functions are strictly increasing or decreasing:
(x + 1)3 (x − 3)3
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
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) = x3 − 6x2 − 36x + 2 ?
Show that f(x) = cos2 x is a decreasing function on (0, π/2) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4)?
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
f(x) = 2x − tan−1 x − log \[\left\{ x + \sqrt{x^2 + 1} \right\}\] is monotonically increasing when
Show that the function f given by f(x) = tan–1 (sin x + cos x) is decreasing for all \[x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) .\]
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 the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing.
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.
Find the values of x for which the following functions are strictly decreasing:
f(x) = 2x3 – 3x2 – 12x + 6
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the values of x for which Revenue is increasing.
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
The function f(x) = 9 - x5 - x7 is decreasing for
The function f(x) = x3 - 3x is ______.
The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
In case of decreasing functions, slope of tangent and hence derivative is ____________.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
The length of the longest interval, in which the function `3 "sin x" - 4 "sin"^3"x"` is increasing, is ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
Let f(x) be a function such that; f'(x) = log1/3(log3(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
A function f is said to be increasing at a point c if ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
