A) 0
B) a
C) -a
D) Does not exist
Correct Answer: A
Solution :
[a] Given \[f'(a)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(a-h)-f(a)}{-h}=0....(1)\] Now \[f'(-{{a}^{-}})=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(-a-h)-f(-a)}{-h}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{-f(a+h)+f(a)}{-h}\] [\[\because \,\,f(x)\] is odd function] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{-f(a-h)+f(a)}{-h}\] \[[\because \,f(2a-x)=f(x)\Rightarrow f(a+x)=f(a-x)]\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(a-h)-f(a)}{h}=0\] [From (1)]
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