## anonymous one year ago Given f '(x) = (5 − x)(8 − x), determine the intervals on which f(x) is increasing or decreasing

1. Jhannybean

This might help.

2. Jhannybean

Find your critical points and then test values to the let and right of them to see where your function is increasing and decreasing as it approaches the critical points.

3. anonymous

$f \prime(x)=0 ~gives~x=5,8$ $f \prime \prime \left( x \right)=\left( 5-x \right)*1-1\left( x-8 \right)=5-x-x+8=13-2x$ at x=5 $f \prime \prime \left( x \right)=13-10=3>0$ so at x=5,there is minima at x=8 $f \prime \prime \left( x \right)=13-16=-3<0$ so there is maxima at x=8 |dw:1441336369747:dw|