WBJEE · Maths · Application of Derivatives
The Rolle's theorem is applicable in the interval \(-1 \leq \mathrm{x} \leq 1\) for the function
- A \(f(x)=x\)
- B \(f(x)=x^2\)
- C \(\mathrm{f}(\mathrm{x})=2 \mathrm{x}^3+3\)
- D \(\mathrm{f}(\mathrm{x})=|\mathrm{x}|\)
Answer & Solution
Correct Answer
(B) \(f(x)=x^2\)
Step-by-step Solution
Detailed explanation
Hints : \(f(x)=x^2 \mid\) and \(\mathrm{f}(1)=\mathrm{f}(-1)\) for \(\mathrm{f}(\mathrm{x})=|\mathrm{x}|\) but at \(\mathrm{x}=0, \mathrm{f}(\mathrm{x})=|\mathrm{x}|\) is not differentiable hence (2) is the correct option. \[ f(1)=1=f(-1) \]
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