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

The extreme f(x)=(x+3)^2e^{-x} is Minimum(-3,0),Maximum(-1,4e)

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

extreme points

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

Minimum (- 3, 0), Maximum (- 1, 4 e)

Solution steps

f^{'} (x) = - e^{- x} (3 + x) (x + 1)

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < - 1,

Decreasing

: - 1 < x < \infty

Plug

x = - 3

into

(x + 3)^{2} e^{- x} : 0

Minimum (- 3, 0)

Plug

x = - 1

into

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

Maximum (- 1, 4 e)

Minimum (- 3, 0), Maximum (- 1, 4 e)

y = \frac{- 3 x}{x ^{2} + 2}

f (x) = 2 π r^{2} + \frac{1500}{r}

(x^{2} + 10) (4 - x^{2})

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

x^{3} + 2 x^{2} - x - 2

What is the extreme f(x)=(x+3)^2e^{-x} ?
The extreme f(x)=(x+3)^2e^{-x} is Minimum(-3,0),Maximum(-1,4e)