Question

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

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

Answer: (B)

$5$

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

$\therefore$ $f^1\left(1\right)=\underset{h\to 0}{lim}$ $\frac{f(1+h)-f\left(1\right)}{h}=\underset{h\to 0}{lim}$ $\frac{1}{h}f(1+h)=5$ [B]