What is the extreme f(x)=-3(x+2)e^{4x},(-5,0) ?

The extreme f(x)=-3(x+2)e^{4x},(-5,0) is Maximum(-9/4 , 3/(4e^9))

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extreme f(x)=-3(x+2)e^{4x},(-5,0)

extreme

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

Solution steps

Find the critical points:

x = - \frac{9}{4}

Domain of

- 3 (x + 2) e^{4 x}, (- 5, 0) : - 5 < x < 0

Find intervals:

Increasing

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

Decreasing

: - \frac{9}{4} < x < 0

Plug the extreme point

x = - \frac{9}{4}

into

- 3 (x + 2) e^{4 x} \Rightarrow y = \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},(-5,0) ?
The extreme f(x)=-3(x+2)e^{4x},(-5,0) is Maximum(-9/4 , 3/(4e^9))