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

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

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

extreme

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

Solution steps

Find the critical points:

x = - \frac{1}{2}

Domain of

- 2 (- 3 x - 3) e^{- 2 x} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < \infty

Plug the extreme point

x = - \frac{1}{2}

into

- 2 (- 3 x - 3) e^{- 2 x} \Rightarrow y = 3 e

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

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