calculus

If f''(x)=-4sin2x, f(0)=0 and f'(0)=2, find the value of f(pi/4).

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  1. f'(x) = 2cos 2x + c
    f'(0) = 2 ----> 0 = 2cos 0 + c
    2 = 2 + c
    c = 0

    so f'(x) = 2cos 2x

    then
    f(x) = sin 2x + k
    f(0) = 0 ----> 0 = sin 0 + k
    k = 0
    so
    f(x) = sin 2x
    f(π/4) = sin 2π/4 = 1

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