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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