Question
Find all critical points of the function.
f(x) = xe^3x
so x= ?
Show steps or tell me how I find them?
f(x) = xe^3x
so x= ?
Show steps or tell me how I find them?
Answers
MathMate
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<sup>3x</sup>
f'(x)=xe<sup>3x</sup> + e<sup>3x</sup>
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<sup>3x</sup>=0. The latter condition requires x to be outside the domain (x=-∞).
Therefore the only critical point is x=-(1/3).
If the interval is not given, it is usually understood to be (-∞, ∞).
f(x)=xe<sup>3x</sup>
f'(x)=xe<sup>3x</sup> + e<sup>3x</sup>
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<sup>3x</sup>=0. The latter condition requires x to be outside the domain (x=-∞).
Therefore the only critical point is x=-(1/3).