Calculus
posted by Nancy on .
Find all critical points of the function.
f(x) = xe^3x
so x= ?
Show steps or tell me how I find them?

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).