What is the extreme y=-1/3 e^{-3x}x-10/9 e^{-3x} ?

The extreme y=-1/3 e^{-3x}x-10/9 e^{-3x} is Minimum(-3,e^9-(10e^9)/9)

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extreme y=-1/3 e^{-3x}x-10/9 e^{-3x}

extreme

Minimum (- 3, e^{9} - \frac{10 e ^{9}}{9})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < \infty

Plug

x = - 3

into

- \frac{1}{3} e^{- 3 x} x - \frac{10}{9} e^{- 3 x} : e^{9} - \frac{10 e ^{9}}{9}

Minimum (- 3, e^{9} - \frac{10 e ^{9}}{9})

What is the extreme y=-1/3 e^{-3x}x-10/9 e^{-3x} ?
The extreme y=-1/3 e^{-3x}x-10/9 e^{-3x} is Minimum(-3,e^9-(10e^9)/9)