Question

Find all critical points of the function.
f(x) = xe^3x

so x= ?

Show steps or tell me how I find them?

Answer 1

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).