Finding critical points?

Question

okay, it gives you f(x)= xe^(2x) and tells you to find all of the critical points

I set the derivative equal to 0, so I have x(2e^2x)+e^(2x)=0, but I am having trouble solving...help please

Answer 1

Hello,
Factor out an e^(2x) giving us e^(2x)*(2x +1) = 0 so e^(2x) = 0 and 1 + 2x = 0 No solution for the first one ans x = -1/2 for the second one. We have (-1/2) * e^(-1) = -1/(2e).

Hope This Helps!