JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f : R \to R\) be differentiable at \(c \in R\) and \(f(c) = 0\). If \(g\left( x \right) = \left| {f\left( x \right)} \right|\) , then at \(x =c, g\) is
- A differentiable if \(f'(c) = 0\)
- B differentiable if \(f'(c) \ne 0\)
- C not differentiable
- D not differentiable if \(f'(c) = 0\)
Answer & Solution
Correct Answer
(A) differentiable if \(f'(c) = 0\)
Step-by-step Solution
Detailed explanation
\(g'\left( c \right) = \mathop {\lim }\limits_{h \to 0} \frac{{\left| {f\left( {c + h} \right)} \right| - \left| {f\left( c \right)} \right|}}{h}\) \(\because \) \(f(c)=0\) \( = \mathop {\lim }\limits_{h \to 0} \frac{{\left| {f\left( {c + h} \right)} \right|}}{h}\)…
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