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Popular >

extreme x^3e^{3x}

Solution

extreme points

x^{3} e^{3 x}

Solution

Minimum (- 1, - \frac{1}{e ^{3}}), Saddle (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - \frac{1}{e ^{3}})

Plug

x = 0

into

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

Saddle (0, 0)

Minimum (- 1, - \frac{1}{e ^{3}}), Saddle (0, 0)

Popular Examples

intercepts of x^3-x intercepts

x^{3} - x

inverse of f(x)= 1/2 (x-4)^3 inverse

f (x) = \frac{1}{2} (x - 4)^{3}

domain of sqrt(2x-x^2)domain

2 x - x^{2}

domain of f(x)=5-2x^2 domain

f (x) = 5 - 2 x^{2}

inverse of x^2-4 inverse

x^{2} - 4

Frequently Asked Questions (FAQ)

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