Question

f(x)= sqrt10x
(f(x+h)-f(x))/h)
Help me please.

Answer 1

\[f(x)=\sqrt{10x}~~\Rightarrow~~f(x+h)=\sqrt{10(x+h)}=\sqrt{10x+10h}\]
Plugging into the difference quotient, you have
\[\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{10x+10h}-\sqrt{10x}}{h}\]
Try to see if you can simplify that. Hint: Multiply top and bottom by the conjugate of the numerator.