Question

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

Answer 1

This might help.

Answer 2

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.

Answer 3

\[f \prime(x)=0 ~gives~x=5,8\]
\[f \prime \prime \left( x \right)=\left( 5-x \right)*1-1\left( x-8 \right)=5-x-x+8=13-2x\]
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