Mathematics - Differentiation Question with Solution | TestHub

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