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Popular >

extreme f(x)=3x^2e^x

Solution

extreme points

f (x) = 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)

Popular Examples

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f (x) = 4 y^{2} - 5 x = 2 y - 3 y^{2}

extreme f(x,y)=x^3-y^3-6xy-4 extreme points

f (x, y) = x^{3} - y^{3} - 6 x y - 4

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

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

extreme f(x,y)=y^3x^5+yx extreme points

f (x, y) = y^{3} x^{5} + y x

extreme f(x,y)=2x^3-2y^3+12xy+3 extreme points

f (x, y) = 2 x^{3} - 2 y^{3} + 12 x y + 3

Frequently Asked Questions (FAQ)

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