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Calculus

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Identify the coordinates of any local extrema of the function y=e^x - e^(2x).

  • Calculus - ,

    Let
    f(x)=ex - e2x
    the domain of f(x) is (-∞,∞).
    Thus the extrema of f(x) can be found at point(s) where f'(x)=0.
    f'(x)=ex - 2e2x
    and f'(x)=0 when
    ex = 2e2x
    2ex=1
    x=ln(1/2) (only root)
    Since f"(x)=ex - 4e2x
    and
    f"(-ln(1/2)) = -1/2
    we conclude that a maximum exists at x=ln(1/2) since f" is negative.

    Can you take it from here?

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