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Popular Functions >

extreme f(x)=x^3e^x

Solution

extreme points

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

Solution

Minimum (- 3, - \frac{27}{e ^{3}}), Saddle (0, 0)

Solution steps

f^{'} (x) = 3 x^{2} e^{x} + e^{x} x^{3}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{3} e^{x} : - \frac{27}{e ^{3}}

Minimum (- 3, - \frac{27}{e ^{3}})

Plug

x = 0

into

x^{3} e^{x} : 0

Saddle (0, 0)

Minimum (- 3, - \frac{27}{e ^{3}}), Saddle (0, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3e^x ?
The extreme f(x)=x^3e^x is Minimum(-3,-(27)/(e^3)),Saddle(0,0)