Suppose $f(x)$ is differentiable $x=1$ and $\lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5$, then…
Suppose $f(x)$ is differentiable $x=1$ and $\lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5$, then $f^{\prime}(1)$ equals
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Solution
$f^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h}$; As function is differentiable so it is continuous as it is given that $\lim _{h \rightarrow 0} \frac{f(1+h)}{h}=5$ and hence $f(1)=0$
Hence $f^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)}{h}=5$
Hence (C) is the correct answer.