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Popular Functions >

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

Solution

extreme points

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

Solution

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

Increasing

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

Plug

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

into

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

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

Plug

x = 0

into

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

Maximum (0, 0)

Plug

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

into

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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