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Popular >

extreme x^3-3x^2+2

Solution

extreme points

x^{3} - 3 x^{2} + 2

Solution

Maximum (0, 2), Minimum (2, - 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

x^{3} - 3 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = 2

into

x^{3} - 3 x^{2} + 2 : - 2

Minimum (2, - 2)

Maximum (0, 2), Minimum (2, - 2)

Popular Examples

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

extreme f(x)=x^3+4x^2+5x-2 extreme points

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extreme 3x^2y+y^3-3x^2-3y^2+2 extreme points

3 x^{2} y + y^{3} - 3 x^{2} - 3 y^{2} + 2

extreme f(x,y)=4x^2+4y^2-4x-8y extreme points

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extreme f(x,y)=10xy-5x^2-7y^2+40x extreme points

f (x, y) = 10 x y - 5 x^{2} - 7 y^{2} + 40 x

Frequently Asked Questions (FAQ)

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