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Let \mathrm{f(x)=|x-a| \varphi(x)}, where j is a continuous function and \mathrm{\varphi(a) \neq 0}. Then

Option: 1

f^{\prime}(a+)=\varphi^{\prime}(a)


Option: 2

f is differentiable at x= a


Option: 3

f^{\prime}(a+)=\varphi^{\prime}(a)


Option: 4

f^{\prime}(a-)=-\varphi(a)


Answers (1)

best_answer

\mathrm{f^{\prime} (a+)=\lim _{h \rightarrow 0+} \frac{|a+h-a| \varphi(a+h)-0}{h} }
               \mathrm{= \lim _{h \rightarrow 0+} \frac{|h| \varphi(a+h)}{h} }
              \mathrm{=\lim _{h \rightarrow 0+} \varphi(a+h)=\varphi(a) }

Similarly \mathrm{f^{\prime}(a-)=-\varphi(a)}.

Posted by

Kuldeep Maurya

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