Question

Rolle's theorem is applicable in the interval $[-2,2]$ for the function

• A. $f\left(x\right)=x^3$
• B. $f\left(x\right)=4X^4$
• C. $f\left(x\right)=2X^3+3$
• D. $f\left(x\right)=\pi \left|x\right|$

Answer 1

Answer: (B)

If we take $f(x)=4x^4$, then
(i) $f(x)$ is continuous in $(-2,2)$
(ii) $f(x)$ is differentiable in $(-2,2)$
(iii) $f(-2)=f(2)$
So, $f(x)=4x^4$ satisfies all the conditions of Rolle's theorem therefore $\exists$ a point $c$ such that $f^{\prime }(c)=0$
$\Rightarrow 16c^3=0\Rightarrow c=0\in (-2,2)$