what would be the maximum value of the function

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

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- Jun 10th 2009, 12:43 PMemmalou264quotient rule
what would be the maximum value of the function

f (x) = 20x/ 5 + x^2 - Jun 10th 2009, 12:52 PMcraig
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 ;)