WBJEE · Maths · Application of Derivatives
Rolle's theorem is applicable in the interval [-2,2] for the function
- A \(f(x)=x^{3}\)
- B \(f(x)=4 x^{4}\)
- C \(f(x)=2 x^{3}+3\)
- D \(f(x)=\pi|x|\)
Answer & Solution
Correct Answer
(B) \(f(x)=4 x^{4}\)
Step-by-step Solution
Detailed explanation
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 \(f^{\prime}(c)=0\)…
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