what would be the maximum value of the function
f (x) = 20x/ 5 + x^2
Seeing as the title of your thread is quotient rule, I'll presume that you know how to find the maximum value of a function, and it's the quotient rule you are stuck on.
First define your two functions, lets call $\displaystyle g(x) = 20x$, $\displaystyle g'(x) = 20$ and $\displaystyle h(x) = 5 + x^2$, $\displaystyle h'(x) = 2x$
The quotient rules states that for a function, $\displaystyle f(x) = \frac{g(x)}{h(x)}$, $\displaystyle f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2}$, which gives you:
$\displaystyle f'(x) = \frac{20(5 + x^2) - 20x(2x)}{(5+x^2)^2}$
I'll leave the rest to you