Q92 / 160 · WBJEE 2012 · Mathematics

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

  • A
    $f(x)=x^{3}$
  • Correct answer
    B
    $f(x)=4 x^{4}$
  • C
    $f(x)=2 x^{3}+3$
  • D
    $f(x)=\pi|x|$

Solution

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

Hence, the correct answer is option: 'B'.

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