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

The extreme f(x)=-xe^{-x}-4e^{-x} is Minimum(-3,-e^3)

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extreme f(x)=-xe^{-x}-4e^{-x}

extreme points

f (x) = - x e^{- x} - 4 e^{- x}

Minimum (- 3, - e^{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < \infty

Plug

x = - 3

into

- x e^{- x} - 4 e^{- x} : - e^{3}

Minimum (- 3, - e^{3})

f (x) = 20 x^{3} + 9 x^{2} - 24 x + 12

f (x) = x^{2} + 9 x + 14

f (x) = - x^{2} - 5 x + 1

f (x) = \frac{x ^{4}}{4} - \frac{4 x ^{3}}{3} + 2 x^{2} - 1

- 30 x^{2} - 25 y^{2} + 480 x + 300 y + 170

What is the extreme f(x)=-xe^{-x}-4e^{-x} ?
The extreme f(x)=-xe^{-x}-4e^{-x} is Minimum(-3,-e^3)