What is the extreme f(x)=xe^{x/3} ?

The extreme f(x)=xe^{x/3} is Minimum(-3,-3/e)

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extreme f(x)=xe^{x/3}

extreme points

f (x) = x e^{\frac{x}{3}}

Minimum (- 3, - \frac{3}{e})

Solution steps

Find the critical points:

x = - 3

Domain of

x e^{\frac{x}{3}} : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < \infty

Plug the extreme point

x = - 3

into

x e^{\frac{x}{3}} \Rightarrow y = - \frac{3}{e}

Minimum (- 3, - \frac{3}{e})

f (x) = x^{4} - 4 x^{3}, - 1 \leq x \leq 4

f (x) = e^{x^{2} - 3 x - 1} [- 3.3]

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

f (x) = \frac{4 x ^{2}}{x - 8}

f (x) = - 2 x^{2} + 12 x + 3

What is the extreme f(x)=xe^{x/3} ?
The extreme f(x)=xe^{x/3} is Minimum(-3,-3/e)