What is the extreme y=-2x^2e^{-2x}-2 ?

The extreme y=-2x^2e^{-2x}-2 is Maximum(0,-2),Minimum(1,-2/(e^2)-2)

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extreme y=-2x^2e^{-2x}-2

extreme points

y = - 2 x^{2} e^{- 2 x} - 2

Maximum (0, - 2), Minimum (1, - \frac{2}{e ^{2}} - 2)

Solution steps

f^{'} (x) = 4 e^{- 2 x} x (x - 1)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

- 2 x^{2} e^{- 2 x} - 2 : - 2

Maximum (0, - 2)

Plug

x = 1

into

- 2 x^{2} e^{- 2 x} - 2 : - \frac{2}{e ^{2}} - 2

Minimum (1, - \frac{2}{e ^{2}} - 2)

Maximum (0, - 2), Minimum (1, - \frac{2}{e ^{2}} - 2)

f (x) = x (22 - 37 + 2 x) (\frac{37}{2} - x)

f (x) = x^{8} e^{x} - 5

f (x) = \frac{1}{2} x e^{- 5 x^{2}}

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

f (x) = 2 x^{3} - 36 x^{2} + 162 x + 3

What is the extreme y=-2x^2e^{-2x}-2 ?
The extreme y=-2x^2e^{-2x}-2 is Maximum(0,-2),Minimum(1,-2/(e^2)-2)