# Thread: increasing or decreasing function

1. ## increasing or decreasing function

for f(x)=x^4-32x+4 find where f'(x)=0, the intervals for which the function increase and decrease, and all the local extrema

2. Originally Posted by euclid2
for f(x)=x^4-32x+4 find where f'(x)=0, the intervals for which the function increase and decrease, and all the local extrema
Hi euclid2,

$f'(x)=4x^3-32$

$f'(x)=0\ \Rightarrow\ x^3=\frac{32}{4}=8\ \Rightarrow\ x=2$

$f''(x)=12x^2$

This is positive when x=2, hence it is a minimum
and since there is only one solution for the derivative f'(x)=0, it is the only turning point and therefore the absolute minimum,
there are no local maxima.

f''(x)=0 at x=0, but is always positive otherwise, so the graph is concave up.