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Popular >

extreme 3x^2e^x

Solution

extreme points

3 x^{2} e^{x}

Solution

Maximum (- 2, \frac{12}{e ^{2}}), Minimum (0, 0)

Solution steps

f^{'} (x) = 3 (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

3 x^{2} e^{x} : \frac{12}{e ^{2}}

Maximum (- 2, \frac{12}{e ^{2}})

Plug

x = 0

into

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

Minimum (0, 0)

Maximum (- 2, \frac{12}{e ^{2}}), Minimum (0, 0)

Graph

Popular Examples

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

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extreme f(x)=(ln(x))/(5x),1<= x<= 4 extreme points

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

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

extreme Q(x,y)=xy extreme points

Q (x, y) = x y

Frequently Asked Questions (FAQ)

What is the extreme 3x^2e^x ?
The extreme 3x^2e^x is Maximum(-2,(12)/(e^2)),Minimum(0,0)