What is the extreme f(x)=xe^{(-x^2)/(32)} ?

The extreme f(x)=xe^{(-x^2)/(32)} is Minimum(-4,-4/(e^{1/2)}),Maximum(4, 4/(e^{1/2)})

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extreme f(x)=xe^{(-x^2)/(32)}

extreme points

f (x) = x e^{\frac{- x ^{2}}{32}}

Minimum (- 4, - \frac{4}{e ^{\frac{1}{2}}}), Maximum (4, \frac{4}{e ^{\frac{1}{2}}})

Solution steps

Find the critical points:

x = - 4, x = 4

Domain of

x e^{\frac{- x ^{2}}{32}} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 4,

Decreasing

: 4 < x < \infty

Plug the extreme point

x = - 4

into

x e^{\frac{- x ^{2}}{32}} \Rightarrow y = - \frac{4}{e ^{\frac{1}{2}}}

Minimum (- 4, - \frac{4}{e ^{\frac{1}{2}}})

Plug the extreme point

x = 4

into

x e^{\frac{- x ^{2}}{32}} \Rightarrow y = \frac{4}{e ^{\frac{1}{2}}}

Maximum (4, \frac{4}{e ^{\frac{1}{2}}})

Minimum (- 4, - \frac{4}{e ^{\frac{1}{2}}}), Maximum (4, \frac{4}{e ^{\frac{1}{2}}})

2400 = 30 x \cdot 10 y

f (- 1.2) = 3 p^{3} + 4 q^{3} - 2 p^{2} q - 4 p - 5 q

f (x) = 8 e x - y - 5 x y + 6 y^{2}

f (x) = - \frac{1}{50} x^{2} + 1.85 x - 8.5

f (x) = 2 x^{3} - 3 x^{2} - 6 x

What is the extreme f(x)=xe^{(-x^2)/(32)} ?
The extreme f(x)=xe^{(-x^2)/(32)} is Minimum(-4,-4/(e^{1/2)}),Maximum(4, 4/(e^{1/2)})