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Popular >

extreme f(x)=x^4+x^3-3x^2+1

Solution

extreme points

f (x) = x^{4} + x^{3} - 3 x^{2} + 1

Solution

Minimum (\frac{- 3 - 105}{8}, - \frac{3 ( 537 + 35 105 )}{512} + 1), Maximum (0, 1), Minimum (\frac{- 3 + 105}{8}, \frac{3 ( 35 105 - 537 )}{512} + 1)

Solution steps

f^{'} (x) = 4 x^{3} + 3 x^{2} - 6 x

Find intervals:

Decreasing

: - \infty < x < \frac{- 3 - 105}{8},

Increasing

: \frac{- 3 - 105}{8} < x < 0,

Decreasing

: 0 < x < \frac{105 - 3}{8},

Increasing

: \frac{105 - 3}{8} < x < \infty

Plug

x = \frac{- 3 - 105}{8}

into

x^{4} + x^{3} - 3 x^{2} + 1 : - \frac{3 ( 537 + 35 105 )}{512} + 1

Minimum (\frac{- 3 - 105}{8}, - \frac{3 ( 537 + 35 105 )}{512} + 1)

Plug

x = 0

into

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

Maximum (0, 1)

Plug

x = \frac{- 3 + 105}{8}

into

x^{4} + x^{3} - 3 x^{2} + 1 : \frac{3 ( 35 105 - 537 )}{512} + 1

Minimum (\frac{- 3 + 105}{8}, \frac{3 ( 35 105 - 537 )}{512} + 1)

Minimum (\frac{- 3 - 105}{8}, - \frac{3 ( 537 + 35 105 )}{512} + 1), Maximum (0, 1), Minimum (\frac{- 3 + 105}{8}, \frac{3 ( 35 105 - 537 )}{512} + 1)

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Frequently Asked Questions (FAQ)

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