What is the extreme f(x)=(x+1)e^{2x} ?

The extreme f(x)=(x+1)e^{2x} is Minimum(-3/2 ,-1/(2e^3))

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extreme f(x)=(x+1)e^{2x}

extreme

Minimum (- \frac{3}{2}, - \frac{1}{2 e ^{3}})

Solution steps

f^{'} (x) = e^{2 x} (2 x + 3)

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{2},

Increasing

: - \frac{3}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

(x + 1) e^{2 x} : - \frac{1}{2 e ^{3}}

Minimum (- \frac{3}{2}, - \frac{1}{2 e ^{3}})

What is the extreme f(x)=(x+1)e^{2x} ?
The extreme f(x)=(x+1)e^{2x} is Minimum(-3/2 ,-1/(2e^3))