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Popular >

extreme x^3-2x^2

Solution

extreme points

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

Solution

Maximum (0, 0), Minimum (\frac{4}{3}, - \frac{32}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4}{3},

Increasing

: \frac{4}{3} < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{4}{3}

into

x^{3} - 2 x^{2} : - \frac{32}{27}

Minimum (\frac{4}{3}, - \frac{32}{27})

Maximum (0, 0), Minimum (\frac{4}{3}, - \frac{32}{27})

Popular Examples

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

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extreme y=xsqrt(4-x^2)extreme points

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extreme (-x^3-x+5)/(2x^3+3x^2-7)extreme points

\frac{- x ^{3} - x + 5}{2 x ^{3} + 3 x ^{2} - 7}

extreme y= x/2+2/x extreme points

y = \frac{x}{2} + \frac{2}{x}

extreme f(x)=(2x-2)/(x^2-10x+25)extreme points

f (x) = \frac{2 x - 2}{x ^{2} - 10 x + 25}

Frequently Asked Questions (FAQ)

What is the extreme x^3-2x^2 ?
The extreme x^3-2x^2 is Maximum(0,0),Minimum(4/3 ,-32/27)