Find the absolute maximum value and the absol | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given function is $f(x) = x^{3}$.$	herefore f^{\prime}(x) = 3x^{2}$.Now,setting $f^{\prime}(x) = 0$ gives $3x^{2} = 0$,which implies $x = 0$.

Vedclass · Accepted Answer

Absolute maximum value is $8$ and absolute minimum value is $-8$.

Vedclass · Answer

(A) The given function is $f(x) = x^{3}$.$	herefore f^{\prime}(x) = 3x^{2}$.Now,setting $f^{\prime}(x) = 0$ gives $3x^{2} = 0$,which implies $x = 0$.We evaluate the value of $f$ at the critical point $x = 0$ and at the endpoints of the interval $[-2, 2]$:$f(0) = 0^{3} = 0$.$f(-2) = (-2)^{3} = -8$.$f(2) = (2)^{3} = 8$.Comparing these values,the absolute maximum value of $f$ on $[-2, 2]$ is $8$ (at $x = 2$) and the absolute minimum value of $f$ on $[-2, 2]$ is $-8$ (at $x = -2$).

Find the absolute maximum value and the absolute minimum value of the function given by $f(x) = x^{3}, x \in [-2, 2]$.

Similar Questions

Find two numbers whose sum is $24$ and whose product is as large as possible.

If $f(x) = x + \frac{1}{x}$ for $x > 0$,then its greatest value is:

If the lengths of three sides of a trapezium other than the base are equal to $10 \ cm$,find the maximum area of the trapezium.

The set of all real values of $\lambda$ for which the function $f(x) = (1 - \cos^2 x)(\lambda + \sin x)$ for $x \in (-\frac{\pi}{2}, \frac{\pi}{2})$ has exactly one maxima and exactly one minima is

Vedclass Test Series

Exam Paper Generator

Online Exam Module