Question

If $f\left(x\right)=\sqrt{x}g\left(x\right)$, where $g\left(4\right)=2$ and $g^{\prime }\left(4\right)=3$, find $f^{\prime }\left(4\right)$.

• A. 6.5
• B. 7.5
• C. 8.5
• D. 9.5

Answer 1

The correct option is A 6.5

$f^{\prime }\left(x\right)=\sqrt{x}{g}^{\prime }\left(x\right)+\left(g\right(x\left)\right)/\left(2\sqrt{x}\right)$
$f^{\prime }\left(4\right)=\sqrt{4}{g}^{\prime }\left(4\right)+\left(g\right(4\left)\right)/\left(2\sqrt{4}\right)=2\times 3+2/(2\times 2)=6.5$