Advertisements
Advertisements
प्रश्न
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
Advertisements
उत्तर
f(x) = 2x3 – 15x2 + 36x + 1
∴ f'(x) = 6x2 – 30x + 36
= 6(x2 – 5x + 6)
= 6(x – 3)(x – 2)
f(x) is an increasing function, if f'(x) > 0
∴ 6(x – 3)(x – 2) > 0
∴ (x – 3) (x – 2) > 0
ab > 0 ⇔ a > 0 and b > 0 or a < 0 and b < 0
∴ Either (x – 3) > 0 and (x – 2) > 0
or
(x – 3) < 0 and (x – 2) < 0
Case 1: x – 3 > 0 and x – 2 > 0
∴ x > 3 and x > 2
∴ x > 3
Case 2: x – 3 < 0 and x – 2 < 0
∴ x < 3 and x < 2
∴ x < 2
Thus, f(x) is an increasing function for x < 2 or x > 3 ,i.e., (– ∞, 2) ∪ (3, ∞)
संबंधित प्रश्न
Find the values of x for `y = [x(x - 2)]^2` is an increasing function.
Which of the following functions are strictly decreasing on `(0, pi/2)`?
- cos x
- cos 2x
- cos 3x
- tan x
Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2].
Without using the derivative, show that the function f (x) = | x | is.
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 0) .
Find the interval in which the following function are increasing or decreasing f(x) = 6 − 9x − x2 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 12x2 + 18x + 15 ?
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) = x4 − 4x3 + 4x2 + 15 ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
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) ?
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
The function f(x) = xx decreases on the interval
Let f(x) = x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then, a and b satisfy.
If the function f(x) = cos |x| − 2ax + b increases along the entire number scale, then
The function f(x) = x9 + 3x7 + 64 is increasing on
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
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
The total cost of manufacturing x articles is C = 47x + 300x2 − x4. Find x, for which average cost is increasing.
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 following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
Find the values of x for which the following functions are strictly decreasing : f(x) = x3 – 9x2 + 24x + 12
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 ______
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 ____________.
Which of the following graph represent the strictly increasing function.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
