What is the extreme sqrt(x-2)e^{-x/2} ?

The extreme sqrt(x-2)e^{-x/2} is Minimum(2,0),Maximum(3, 1/(e^{3/2)})

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extreme sqrt(x-2)e^{-x/2}

extreme

Minimum (2, 0), Maximum (3, \frac{1}{e ^{\frac{3}{2}}})

Solution steps

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

Find intervals:

Increasing

: 2 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 2

into

x - 2 e^{- \frac{x}{2}} : 0

Minimum (2, 0)

Plug

x = 3

into

x - 2 e^{- \frac{x}{2}} : \frac{1}{e ^{\frac{3}{2}}}

Maximum (3, \frac{1}{e ^{\frac{3}{2}}})

Minimum (2, 0), Maximum (3, \frac{1}{e ^{\frac{3}{2}}})

What is the extreme sqrt(x-2)e^{-x/2} ?
The extreme sqrt(x-2)e^{-x/2} is Minimum(2,0),Maximum(3, 1/(e^{3/2)})