Calculus
posted by Robin .
Find the absolute maximum and the absolute minimum values of
f(x)=x−7cos(x) on the interval [−ð,ð).

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)=07=07 = 7
f(π)=π+7 = 10.14 (approx.)
from which you can pick out the absolute maximum and minimum.
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