What is the extreme f(x)=-3(x+2)e^{4x} ?

The extreme f(x)=-3(x+2)e^{4x} is Maximum(-9/4 , 3/(4e^9))

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extreme f(x)=-3(x+2)e^{4x}

extreme

Maximum (- \frac{9}{4}, \frac{3}{4 e ^{9}})

Solution steps

f^{'} (x) = - 3 (4 e^{4 x} x + 9 e^{4 x})

Find intervals:

Increasing

: - \infty < x < - \frac{9}{4},

Decreasing

: - \frac{9}{4} < x < \infty

Plug

x = - \frac{9}{4}

into

- 3 (x + 2) e^{4 x} : \frac{3}{4 e ^{9}}

Maximum (- \frac{9}{4}, \frac{3}{4 e ^{9}})

What is the extreme f(x)=-3(x+2)e^{4x} ?
The extreme f(x)=-3(x+2)e^{4x} is Maximum(-9/4 , 3/(4e^9))