Question

Consider the function $f\left(x\right)=\{\begin{array}{cc}{x}^2-5,& x\le 3\\ \sqrt{x+13},& x>3\end{array}$.

Find the differential coefficient of $f\left(x\right)$ at $x=12.$

• A. $\frac{5}{2}$
• B. $5$
• C. $\frac{1}{5}$
• D. $\frac{1}{10}$

Answer 1

The correct option is D $\frac{1}{10}$

$f\left(x\right)=\sqrt{x+13}$ for $x>3$

$f^{\prime }\left(x\right)=\frac{1\times 1}{2\sqrt{x+13}}$

$f^{\prime }\left(12\right)=\frac{1}{2\sqrt{25}}=\frac{1}{2\times 5}$

$=\frac{1}{10}$