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Popular Functions >

extreme 1/4 x^4+1/2 x^3-3x^2+2

Solution

extreme

Solution

Minimum (\frac{- 3 - 105}{4}, - \frac{3 ( 537 + 35 105 )}{128} + 2), Maximum (0, 2), Minimum (\frac{- 3 + 105}{4}, \frac{3 ( 35 105 - 537 )}{128} + 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 105}{4},

Increasing

: \frac{- 3 - 105}{4} < x < 0,

Decreasing

: 0 < x < \frac{105 - 3}{4},

Increasing

: \frac{105 - 3}{4} < x < \infty

Plug

x = \frac{- 3 - 105}{4}

into

\frac{1}{4} x^{4} + \frac{1}{2} x^{3} - 3 x^{2} + 2 : - \frac{3 ( 537 + 35 105 )}{128} + 2

Minimum (\frac{- 3 - 105}{4}, - \frac{3 ( 537 + 35 105 )}{128} + 2)

Plug

x = 0

into

\frac{1}{4} x^{4} + \frac{1}{2} x^{3} - 3 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = \frac{- 3 + 105}{4}

into

\frac{1}{4} x^{4} + \frac{1}{2} x^{3} - 3 x^{2} + 2 : \frac{3 ( 35 105 - 537 )}{128} + 2

Minimum (\frac{- 3 + 105}{4}, \frac{3 ( 35 105 - 537 )}{128} + 2)

Minimum (\frac{- 3 - 105}{4}, - \frac{3 ( 537 + 35 105 )}{128} + 2), Maximum (0, 2), Minimum (\frac{- 3 + 105}{4}, \frac{3 ( 35 105 - 537 )}{128} + 2)

Graph

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Frequently Asked Questions (FAQ)

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