Find the absolute maximum and the absolute minimum values of

Question

f(x)=x−7cos(x) on the interval [−ð,ð).

Answer 1

Think of
f(x)=f1(x)+f2(x)
where
f1(x)=x
f2(x)=-cos(x)

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.