Question

Find the local extrema of f

(x^2)/sqrt(x+7)

Answer 1

u have
\[ \large f(x)=\frac{x^2}{\sqrt{x+7}} \]
find f'(x) (the first derivative)

Answer 2

I got

\[(2x \sqrt{x+7}-(x^2)/2)\div((x+7)\sqrt{x+7})\]

Answer 3

is this correct?

Answer 4

\[ \large f'(x)=\frac{2x\sqrt{x+7}-x^2\frac{1}{2\sqrt{x+7}}}{x+7} \]