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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