For f f(x) = 2xe^2x
Find the absolute minimum and justify it.
I found it to be (-1/2, -1/e) from its derivative = 0.
However, that just justifies it as an extrema and I normally say that it is a minimum because the derivative goes from negative to positive.
However, the derivative starts at 0 so it doesn't work anymore.

Question

For f f(x) = 2xe^2x
Find the absolute minimum and justify it.
I found it to be (-1/2, -1/e)  from its derivative = 0.
However, that just justifies it as an extrema and I normally say that it is a minimum because the derivative goes from negative to positive.
However, the derivative starts at 0 so it doesn't work anymore.

mathmate · Answer

Try to plot the derivative and you'll see that it crosses from negative to positive at the critical point.