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Popular >

extreme f(x)=x^2(x-1)(x+3)

Solution

extreme points

f (x) = x^{2} (x - 1) (x + 3)

Solution

Minimum (\frac{- 3 - 33}{4}, - \frac{3 ( 69 + 11 33 )}{32}), Maximum (0, 0), Minimum (\frac{- 3 + 33}{4}, \frac{3 ( 11 33 - 69 )}{32})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 33}{4},

Increasing

: \frac{- 3 - 33}{4} < x < 0,

Decreasing

: 0 < x < \frac{33 - 3}{4},

Increasing

: \frac{33 - 3}{4} < x < \infty

Plug

x = \frac{- 3 - 33}{4}

into

x^{2} (x - 1) (x + 3) : - \frac{3 ( 69 + 11 33 )}{32}

Minimum (\frac{- 3 - 33}{4}, - \frac{3 ( 69 + 11 33 )}{32})

Plug

x = 0

into

x^{2} (x - 1) (x + 3) : 0

Maximum (0, 0)

Plug

x = \frac{- 3 + 33}{4}

into

x^{2} (x - 1) (x + 3) : \frac{3 ( 11 33 - 69 )}{32}

Minimum (\frac{- 3 + 33}{4}, \frac{3 ( 11 33 - 69 )}{32})

Minimum (\frac{- 3 - 33}{4}, - \frac{3 ( 69 + 11 33 )}{32}), Maximum (0, 0), Minimum (\frac{- 3 + 33}{4}, \frac{3 ( 11 33 - 69 )}{32})

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Frequently Asked Questions (FAQ)

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