WBJEE · Maths · Continuity and Differentiability
Suppose that \(f(x)\) is a differentiable function such that \(f^{\prime}(x)\) is continuous, \(f^{\prime}(0)=1\) and \(f^{\prime \prime}(0)\) does not exist. Let \(g(x)=x f^{\prime}(x) .\) Then,
- A \(g^{\prime}(0)\) does not exist
- B \(g^{\prime}(0)=0\)
- C \(g^{\prime}(0)=1\)
- D \(g^{\prime}(0)=2\)
Answer & Solution
Correct Answer
(C) \(g^{\prime}(0)=1\)
Step-by-step Solution
Detailed explanation
Given, \(f^{\prime}(0)=1\) and \(f^{\prime \prime}\) " (0) does not exist. Also, given \(g(x)=x f^{\prime}(x)\) \(\therefore \quad g^{\prime}(x)=x f^{\prime \prime}(x)+f^{\prime}(x)\) Put \(x=0,\) we get…
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