What is the extreme 5x^2e^{-x} ?

The extreme 5x^2e^{-x} is Minimum(0,0),Maximum(2,(20)/(e^2))

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extreme 5x^2e^{-x}

extreme points

5 x^{2} e^{- x}

Minimum (0, 0), Maximum (2, \frac{20}{e ^{2}})

Solution steps

Find the critical points:

x = 0, x = 2

Domain of

5 x^{2} e^{- x} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug the extreme point

x = 0

into

5 x^{2} e^{- x} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 2

into

5 x^{2} e^{- x} \Rightarrow y = \frac{20}{e ^{2}}

Maximum (2, \frac{20}{e ^{2}})

Minimum (0, 0), Maximum (2, \frac{20}{e ^{2}})

\frac{( 3 x - 1 )}{x}

f (x) = x^{2} (2 - 4 x)^{3}

f (x, y) = e^{- (x^{2} + y^{2})} (x + y^{2}) + (\frac{1}{2})

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

\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} - 4 x + 8

What is the extreme 5x^2e^{-x} ?
The extreme 5x^2e^{-x} is Minimum(0,0),Maximum(2,(20)/(e^2))