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Popular >

extreme f(x)=x^2e^x

Solution

extreme points

f (x) = x^{2} e^{x}

Solution

Maximum (- 2, \frac{4}{e ^{2}}), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

x^{2} e^{x} : \frac{4}{e ^{2}}

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

Plug

x = 0

into

x^{2} e^{x} : 0

Minimum (0, 0)

Maximum (- 2, \frac{4}{e ^{2}}), Minimum (0, 0)

Popular Examples

extreme f(x)=-x^3+6x^2 extreme points

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

domain of f(x)=sqrt(3x-24)domain

f (x) = 3 x - 24

parity f(x)=sqrt(1/(2x^{3x-1))}parity

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

inverse of 1/2 (x+4)^2-2 inverse

\frac{1}{2} (x + 4)^{2} - 2

extreme f(x)=5+4x-x^3 extreme points

f (x) = 5 + 4 x - x^{3}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^2e^x ?
The extreme f(x)=x^2e^x is Maximum(-2, 4/(e^2)),Minimum(0,0)