Calculus

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

  • Calculus -

    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.

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