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Popular >

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

Solution

extreme points

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

Solution

Maximum (0, 3), Minimum (2, - 1)

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} + 3 : 3

Maximum (0, 3)

Plug

x = 2

into

x^{3} - 3 x^{2} + 3 : - 1

Minimum (2, - 1)

Maximum (0, 3), Minimum (2, - 1)

Popular Examples

extreme f(x,y)=sqrt(48-3x^2-3y^2)extreme points

f (x, y) = 48 - 3 x^{2} - 3 y^{2}

extreme f(x)= x/(x^2+16)extreme points

f (x) = \frac{x}{x ^{2} + 16}

extreme f(x)=xe^{6x^2}extreme points

f (x) = x e^{6 x^{2}}

extreme f(x)=2x^3-6x+4 extreme points

f (x) = 2 x^{3} - 6 x + 4

extreme f(x,y)=x^2y+y^3-75y extreme points

f (x, y) = x^{2} y + y^{3} - 75 y

Frequently Asked Questions (FAQ)

What is the extreme y=x^3-3x^2+3 ?
The extreme y=x^3-3x^2+3 is Maximum(0,3),Minimum(2,-1)