Posted by **Nancy** on Tuesday, June 29, 2010 at 1:27pm.

Find all critical points of the function.

f(x) = xe^3x

so x= ?

Show steps or tell me how I find them?

- Calculus -
**MathMate**, Tuesday, June 29, 2010 at 9:41pm
A critical point is an interior point of an interval of the function at which f'(x)=0 or undefined.

If the interval is not given, it is usually understood to be (-∞, ∞).

f(x)=xe^{3x}

f'(x)=xe^{3x} + e^{3x}

f'(x) is therefore defined within the interval (-∞, ∞).

Now find x for which f'(x)=0

f'(x)=0 when x=-(1/3) or e^{3x}=0. The latter condition requires x to be outside the domain (x=-∞).

Therefore the only critical point is x=-(1/3).

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