Question

If $f\left(x\right)=\frac{x-4}{2\sqrt{x}}$ , then $f^{\prime }\left(1\right)$ is

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $1$
• D. $0$

Answer 1

The correct option is A $\frac{5}{4}$

Given,

$f\left(x\right)=$$\frac{x-4}{2\sqrt{x}}$

diff. $w.r.t$ $x$

$f^{{}^{\prime }}\left(x\right)$$=\frac{x+4}{4x\sqrt{x}}$

put $x=1$

$f^{{}^{\prime }}\left(1\right)$$=\frac{1+4}{4\left(1\right)\sqrt{1}}$

$f^{{}^{\prime }}\left(1\right)=$ $\frac{5}{4}$