Advertisements
Advertisements
प्रश्न
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Advertisements
उत्तर
f(x) = 2x3 - 15x2 - 144x - 7
∴ f'(x) = 6x2 - 30x - 144
f(x) is an increasing function, if f'(x) > 0
∴ 6(x2 - 5x - 24) > 0
∴ 6(x + 3)(x - 8) > 0
∴ (x + 3)(x - 8) > 0
ab > 0 ⇔ a > 0 and b > 0 or a < 0 or b < 0
∴ Either (x + 3) > 0 and (x – 8) > 0 or
(x + 3) < 0 and (x – 8) < 0
Case 1: x + 3 > 0 and x - 8 > 0
∴ x > -3 and x > 8
∴ x > 8
Case 2: x + 3 < 0 and x - 8 < 0
∴ x < - 3 or x < 8
∴ x < - 3
Thus, f(x) is an increasing function for x < -3, or x > 8 i.e., (-∞, - 3) ∪ (8, ∞).
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.
Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R ?
Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?
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) = 2x3 − 12x2 + 18x + 15 ?
Find the interval in which the following function are increasing or decreasing f(x) = 8 + 36x + 3x2 − 2x3 ?
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) = 2x3 − 24x + 107 ?
Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
Let f(x) = x3 − 6x2 + 15x + 3. Then,
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
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
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).
Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R.
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.
Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find the inverse of f: N → S, where S is range of f.
Find the values of x for which the following functions are strictly decreasing:
f(x) = 2x3 – 3x2 – 12x + 6
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
State whether the following statement is True or False:
The function f(x) = `3/x` + 10, x ≠ 0 is decreasing
A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is
Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.
The function f(x) = tanx – x ______.
The function f(x) = x2 – 2x is increasing in the interval ____________.
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
