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).
Answer This Question
Related Questions
 help please!  f(x)=x+1/x Find all critical numbers. Find where the function is ...
 math  find the domain and all the critical points of the function. a) x(the ...
 math  find the domain and all the critical points of the function. a) x(the ...
 Calculus  Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x ...
 Calculus  Given the function: f(x) = x^2 + 1 / x^2  9 a)find y and x ...
 Calculus  For the function below, determine the intervals of concavity: f(x)=...
 calculus  Please help!! *f(x)= x(x+6)^1/2 find two x intercepts. Then show that...
 Calculus  Find the interval(s) where the function is increasing and the ...
 calculus  f(x)= −x2lnx find the critical points , increasing & decreasing...
 Math  How do you find critical points in a function? For example, find the ...
More Related Questions