Advertisements
Advertisements
प्रश्न
Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function
Advertisements
उत्तर
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).
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:
10 − 6x − 2x2
Find the intervals in which the following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Let I be any interval disjoint from (−1, 1). Prove that the function f given by `f(x) = x + 1/x` is strictly increasing on I.
Prove that the function f given by f(x) = log cos x is strictly decreasing on `(0, pi/2)` and strictly increasing on `((3pi)/2, 2pi).`
Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R ?
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) = 6 − 9x − x2 ?
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 \[f\left( x \right) = \frac{3}{10} x^4 - \frac{4}{5} x^3 - 3 x^2 + \frac{36}{5}x + 11\] ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
The function f(x) = xx decreases on the interval
Function f(x) = x3 − 27x + 5 is monotonically increasing when ______.
Find `dy/dx,if e^x+e^y=e^(x-y)`
Find the values of x for which the following func- tions are strictly increasing : f(x) = x3 – 6x2 – 36x + 7
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______
Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
Function given by f(x) = sin x is strictly increasing in.
Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.
If f(x) = x + cosx – a then ______.
Function f(x) = `log(1 + x) - (2x)/(2 + x)` is monotonically increasing when ______.
y = log x satisfies for x > 1, the inequality ______.
Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.
