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Popular Functions >

extreme f(x)=x^2(x-2)(x+3)

Solution

extreme points

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

Solution

Minimum (\frac{- 3 - 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512}), Maximum (0, 0), Minimum (\frac{- 3 + 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Solution steps

f^{'} (x) = x (4 x^{2} + 3 x - 12)

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 201}{8},

Increasing

: \frac{- 3 - 201}{8} < x < 0,

Decreasing

: 0 < x < \frac{201 - 3}{8},

Increasing

: \frac{201 - 3}{8} < x < \infty

Plug

x = \frac{- 3 - 201}{8}

into

x^{2} (x - 2) (x + 3) : - \frac{3 ( 1833 + 67 201 )}{512}

Minimum (\frac{- 3 - 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512})

Plug

x = 0

into

x^{2} (x - 2) (x + 3) : 0

Maximum (0, 0)

Plug

x = \frac{- 3 + 201}{8}

into

x^{2} (x - 2) (x + 3) : \frac{3 ( 67 201 - 1833 )}{512}

Minimum (\frac{- 3 + 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Minimum (\frac{- 3 - 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512}), Maximum (0, 0), Minimum (\frac{- 3 + 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Graph

Popular Examples

intercepts of f(x)=-4(x-2)^2+16

in t erce pt s f (x) = - 4 (x - 2)^{2} + 16

inverse of f(x)=ln(x/(x+2))

in v erse f (x) = ln (\frac{x}{x + 2})

domain of f(x)=2x^2-8x-3

d o main f (x) = 2 x^{2} - 8 x - 3

domain of 3/4 x+7

d o main \frac{3}{4} x + 7

domain of f(x)=2^{x+1}-1

d o main f (x) = 2^{x + 1} - 1

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^2(x-2)(x+3) ?
The extreme f(x)=x^2(x-2)(x+3) is