Advertisements
Advertisements
Question
Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function
Advertisements
Solution
f(x) = 2x3 – 15x2 – 144x – 7
∴ f'(x) = 6x2 – 30x – 144
= 6(x2 – 5x – 24)
= 6(x + 3)(x – 8)
f(x) is a decreasing function, if f'(x) < 0
6(x + 3)(x – 8) < 0
∴ (x + 3)(x – 8) < 0
ab < 0 ⇔ a > 0 and b < 0 or a < 0 and 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
Case 2: x + 3 < 0 and x – 8 > 0
∴ x < – 3 and x > 8, which is not possible
Thus, f(x) is a decreasing function for – 3 < x < 8 ,i.e., (– 3, 8).
RELATED QUESTIONS
Show that y = `log(1+x) - (2x)/(2+x), x> - 1`, is an increasing function of x throughout its domain.
Prove that the logarithmic function is strictly increasing on (0, ∞).
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
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 − 24x + 107 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?
Find the interval in which the following function are increasing or decreasing f(x) = \[5 x^\frac{3}{2} - 3 x^\frac{5}{2}\] x > 0 ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 + 9x + 15 ?
Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
What are the values of 'a' for which f(x) = ax is increasing on R ?
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
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 increasing : f(x) = 2x3 – 3x2 – 12x + 6
Find the values of x for which the following functions are strictly increasing:
f(x) = 3 + 3x – 3x2 + x3
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly decreasing
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
If f(x) = x3 – 15x2 + 84x – 17, then ______.
Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`
Which of the following functions is decreasing on `(0, pi/2)`?
Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.
`"f"("x") = (("e"^(2"x") - 1)/("e"^(2"x") + 1))` is ____________.
The function `"f"("x") = "x"/"logx"` increases on the interval
Let f(x) = `x/sqrt(a^2 + x^2) - (d - x)/sqrt(b^2 + (d - x)^2), x ∈ R` where a, b and d are non-zero real constants. Then ______.
The function f(x) = xex(1 − x), x ∈ R, is ______.
