Homework Help: Calculus

Posted by Abigail on Tuesday, June 15, 2010 at 10:30am.

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

Calculus - MathMate, Tuesday, June 15, 2010 at 7:04pm
Let
f(x)=e^x - e^2x
the domain of f(x) is (-∞,∞).
Thus the extrema of f(x) can be found at point(s) where f'(x)=0.
f'(x)=e^x - 2e^2x
and f'(x)=0 when
e^x = 2e^2x
2e^x=1
x=ln(1/2) (only root)
Since f"(x)=e^x - 4e^2x
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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