WBJEE · Maths · Application of Derivatives
In which of the following functions, Rolle's theorem is applicable?
- A \(f(x)=|x|\) in \(-2 \leq x \leq 2\)
- B \(\mathrm{f}(\mathrm{x})=\tan \mathrm{x}\) in \(0 \leq \mathrm{x} \leq \pi\)
- C \(\mathrm{f}(\mathrm{x})=1+(\mathrm{x}-2)^{\frac{2}{3}}\) in \(1 \leq \mathrm{x} \leq 3\)
- D \(\mathrm{f}(\mathrm{x})=\mathrm{x}(\mathrm{x}-2)^2\) in \(0 \leq \mathrm{x} \leq 2\)
Answer & Solution
Correct Answer
(D) \(\mathrm{f}(\mathrm{x})=\mathrm{x}(\mathrm{x}-2)^2\) in \(0 \leq \mathrm{x} \leq 2\)
Step-by-step Solution
Detailed explanation
Hints: \((\mathrm{A}) \mathrm{f}(\mathrm{x})=|\mathrm{x}|\) not differentiable at \(\mathrm{x}=0\)
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