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Popular Functions >

extreme x^4(x-2)(x+3)

Solution

extreme points

x^{4} (x - 2) (x + 3)

Solution

Minimum (\frac{- 5 - 601}{12}, \frac{- 149737888 - 4634912 601}{2985984}), Maximum (0, 0), Minimum (\frac{- 5 + 601}{12}, \frac{4634912 601 - 149737888}{2985984})

Solution steps

f^{'} (x) = x^{3} (6 x^{2} + 5 x - 24)

Find intervals:

Decreasing

: - \infty < x < \frac{- 5 - 601}{12},

Increasing

: \frac{- 5 - 601}{12} < x < 0,

Decreasing

: 0 < x < \frac{601 - 5}{12},

Increasing

: \frac{601 - 5}{12} < x < \infty

Plug

x = \frac{- 5 - 601}{12}

into

x^{4} (x - 2) (x + 3) : \frac{- 149737888 - 4634912 601}{2985984}

Minimum (\frac{- 5 - 601}{12}, \frac{- 149737888 - 4634912 601}{2985984})

Plug

x = 0

into

x^{4} (x - 2) (x + 3) : 0

Maximum (0, 0)

Plug

x = \frac{- 5 + 601}{12}

into

x^{4} (x - 2) (x + 3) : \frac{4634912 601 - 149737888}{2985984}

Minimum (\frac{- 5 + 601}{12}, \frac{4634912 601 - 149737888}{2985984})

Minimum (\frac{- 5 - 601}{12}, \frac{- 149737888 - 4634912 601}{2985984}), Maximum (0, 0), Minimum (\frac{- 5 + 601}{12}, \frac{4634912 601 - 149737888}{2985984})

Graph

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Frequently Asked Questions (FAQ)

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