Find the critical point of (1 + 2 x) exp(2 x)?

Question

Find the critical point of (1 + 2 x) exp(2 x).
Please do it step by step so i can follow.. i tried this but made a mistake and im trying to find out where i went wrong. Thanks!

ps/ exp(2x) is the same as e^2x

Answer 1

Derivative of the function
f(x) = (1+2x)(exp(2x))
is
f‘(x) = 2 exp(2x) + 2 (1 + 2 x) exp(2 x) = 4 (x+1) exp(2 x)
Critical point is
x = -1
where
f‘(x) = 0.
-

Answer 2

The critical points are found by setting the first derivative equal to zero.

[(1+2x)e^(2x)]'
= (2)e^(2x) + (1+2x)(e^(2x))(2)
= 2e^(2x) [1 + 1+2x]
= 2e^(2x) (2+2x)

Since 2e^(2x) never equals zero, then 2+2x = 0, so x = -1