# Math Help - quotient rule

1. ## quotient rule

what would be the maximum value of the function

f (x) = 20x/ 5 + x^2

2. Originally Posted by emmalou264
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 $g(x) = 20x$, $g'(x) = 20$ and $h(x) = 5 + x^2$, $h'(x) = 2x$

The quotient rules states that for a function, $f(x) = \frac{g(x)}{h(x)}$, $f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2}$, which gives you:

$f'(x) = \frac{20(5 + x^2) - 20x(2x)}{(5+x^2)^2}$

I'll leave the rest to you