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Popular >

extreme x^2e^x

Solution

extreme points

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)=5+54x-2x^3 extreme points

f (x) = 5 + 54 x - 2 x^{3}

extreme f(x,y)=x^2+2y^2+4xy+2x+4y extreme points

f (x, y) = x^{2} + 2 y^{2} + 4 x y + 2 x + 4 y

extreme f(x,y)=2x^2+2xy+y^2+2x-3 extreme points

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

extreme K(y,z)=32yz extreme points

K (y, z) = 32 yz

extreme f(x)=(x^2-1)/(x^2+1)extreme points

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

Frequently Asked Questions (FAQ)

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