Advertisements
Advertisements
प्रश्न
By completing the following activity, find the values of x such that f(x) = 2x3 – 15x2 – 84x – 7 is decreasing function.
Solution: f(x) = 2x3 – 15x2 – 84x – 7
∴ f'(x) = `square`
∴ f'(x) = 6`(square) (square)`
Since f(x) is decreasing function.
∴ f'(x) < 0
Case 1: `(square)` > 0 and (x + 2) < 0
∴ x ∈ `square`
Case 2: `(square)` < 0 and (x + 2) > 0
∴ x ∈ `square`
∴ f(x) is decreasing function if and only if x ∈ `square`
Advertisements
उत्तर
f(x) = 2x3 – 15x2 – 84x – 7
∴ f'(x) = 6x2 – 30x – 84
= 6(x2 – 5x – 14)
∴ f'(x) = 6(x – 7)(x + 2)
Since f(x) is decreasing function.
∴ f'(x) < 0
∴ 6(x – 7)(x + 2) < 0
∴ (x – 7)(x + 2) < 0
Case 1: (x – 7) > 0 and (x + 2) < 0
∴ x > 7 and x < – 2
∴ x ∈ `bb(cancel0)` , which is not possible
Case 2: (x – 7) < 0 and (x + 2) > 0
∴ x < 7 and x > – 2
∴ x ∈ (– 2, 7)
∴ f(x) is decreasing function if and only if x ∈ (– 2, 7).
APPEARS IN
संबंधित प्रश्न
Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.
Find the value of c in Rolle's theorem for the function `f(x) = x^3 - 3x " in " (-sqrt3, 0)`
Find the interval in which the following function are increasing or decreasing f(x) = 5 + 36x + 3x2 − 2x3 ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 − 36x + 2 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 24x + 107 ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x3 + 4x2 + 15 ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4)?
Write the set of values of k for which f(x) = kx − sin x is increasing on R ?
Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?
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) = 2 tan x + (2a + 1) loge | sec x | + (a − 2) x is increasing on R, then
Function f(x) = cos x − 2 λ x is monotonic decreasing when
Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R.
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
The function f(x) = 9 - x5 - x7 is decreasing for
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 ______
The interval on which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
Function given by f(x) = sin x is strictly increasing in.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
