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Popular >

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

Solution

extreme points

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

Solution

Maximum (- 3, 0), Minimum (\frac{- 5 - 145}{10}, - \frac{950 + 58 145}{125}), Maximum (0, 0), Minimum (\frac{- 5 + 145}{10}, \frac{58 145 - 950}{125})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < \frac{- 5 - 145}{10},

Increasing

: \frac{- 5 - 145}{10} < x < 0,

Decreasing

: 0 < x < \frac{145 - 5}{10},

Increasing

: \frac{145 - 5}{10} < x < \infty

Plug

x = - 3

into

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

Maximum (- 3, 0)

Plug

x = \frac{- 5 - 145}{10}

into

(x + 3)^{2} (x^{3} - x^{2}) : - \frac{950 + 58 145}{125}

Minimum (\frac{- 5 - 145}{10}, - \frac{950 + 58 145}{125})

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{- 5 + 145}{10}

into

(x + 3)^{2} (x^{3} - x^{2}) : \frac{58 145 - 950}{125}

Minimum (\frac{- 5 + 145}{10}, \frac{58 145 - 950}{125})

Maximum (- 3, 0), Minimum (\frac{- 5 - 145}{10}, - \frac{950 + 58 145}{125}), Maximum (0, 0), Minimum (\frac{- 5 + 145}{10}, \frac{58 145 - 950}{125})

Graph

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Frequently Asked Questions (FAQ)

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