# where the function is concave down and concave up

• July 27th 2011, 10:48 PM
NeoSonata
where the function is concave down and concave up
f(x) = x^2 / (x^2 - 16)

f'(x) = -32x/(x^2-16)^2

x= -4,0,4

f''(x) = (96x^2 +512) / (x^2 -16)^3

how do i do this?
• July 27th 2011, 10:55 PM
pickslides
Re: where the function is concave down and concave up
Quote:

Originally Posted by NeoSonata

f''(x) = (96x^2 +512) / (x^2 -16)^3

how do i do this?

sub the values for x you found for the stationary points.

If $\displaystyle f''(x_0) > 0 \implies$ min

and $\displaystyle f''(x_0) < 0 \implies$ max