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Popular >

extreme x^3-x^2

Solution

extreme points

x^{3} - x^{2}

Solution

Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{4}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{2}{3}

into

x^{3} - x^{2} : - \frac{4}{27}

Minimum (\frac{2}{3}, - \frac{4}{27})

Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{4}{27})

Popular Examples

extreme f(x,y)=xy+(27)/x+(27)/y extreme points

f (x, y) = x y + \frac{27}{x} + \frac{27}{y}

extreme 2x^3+3x^2-12x+1 extreme points

2 x^{3} + 3 x^{2} - 12 x + 1

extreme f(x)=8x-x^4 extreme points

f (x) = 8 x - x^{4}

extreme f(x)=x^2-2x-4 extreme points

f (x) = x^{2} - 2 x - 4

extreme f(x)=-x^2-6x+9 extreme points

f (x) = - x^{2} - 6 x + 9

Frequently Asked Questions (FAQ)

What is the extreme x^3-x^2 ?
The extreme x^3-x^2 is Maximum(0,0),Minimum(2/3 ,-4/27)