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Popular >

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

Solution

extreme points

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

Solution

Minimum (\frac{- 3 - 73}{8}, - \frac{827 + 73 73}{512}), Maximum (0, 0), Minimum (\frac{- 3 + 73}{8}, \frac{73 73 - 827}{512})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 73}{8},

Increasing

: \frac{- 3 - 73}{8} < x < 0,

Decreasing

: 0 < x < \frac{73 - 3}{8},

Increasing

: \frac{73 - 3}{8} < x < \infty

Plug

x = \frac{- 3 - 73}{8}

into

x^{2} (x - 1) (x + 2) : - \frac{827 + 73 73}{512}

Minimum (\frac{- 3 - 73}{8}, - \frac{827 + 73 73}{512})

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{- 3 + 73}{8}

into

x^{2} (x - 1) (x + 2) : \frac{73 73 - 827}{512}

Minimum (\frac{- 3 + 73}{8}, \frac{73 73 - 827}{512})

Minimum (\frac{- 3 - 73}{8}, - \frac{827 + 73 73}{512}), Maximum (0, 0), Minimum (\frac{- 3 + 73}{8}, \frac{73 73 - 827}{512})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^2(x-1)(x+2) ?
The extreme f(x)=x^2(x-1)(x+2) is