Posted by Robin on .
Find the absolute maximum and the absolute minimum values of
f(x)=x−7cos(x) on the interval [−ð,ð).
We note that f1(x) is monotonically increasing throughout [-π, π) while
f2(x) is increasing between [-π, 0) and decreasing between [0,π).
Therefore to find the absolute maximum and minimum, we only need to check three locations, x=-π, x=0, and x=π.
f(-π)=-π+7 = 3.86 (approx.)
f(0)=0-7=0-7 = -7
f(π)=π+7 = 10.14 (approx.)
from which you can pick out the absolute maximum and minimum.