Question

Suppose $f\left(x\right)$ is differentiable at $x=1$, $f\left(1\right)=0$ and $\underset{h\to 0}{lim}\frac{f(1+h)}{h}=5.$ Then $f^{\prime }\left(1\right)$ equals

• A. $4$
• B. $3$
• C. $6$
• D. $5$

Answer 1

The correct option is D $5$

The right hand derivative is given by:

$f^{\prime }\left(x\right)={lim}_{h\to 0}\frac{f(1+h)-f\left(1\right)}{h}$

Now, $f\left(1\right)=0$

$\Rightarrow f^{\prime }\left(x\right)={lim}_{h\to 0}\frac{f(1+h)-0}{h}$

$\Rightarrow f^{\prime }\left(x\right)={lim}_{h\to 0}\frac{f(1+h)}{h}$

$\Rightarrow f^{\prime }\left(x\right)=5$ .....Answer