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Popular Functions >

extreme 30x^3-19x^2-14x+8

Solution

extreme

Solution

Maximum (\frac{19 - 1621}{90}, \frac{1621 1621 - 42769}{12150} + 8), Minimum (\frac{19 + 1621}{90}, \frac{- 42769 - 1621 1621}{12150} + 8)

Solution steps

f^{'} (x) = 90 x^{2} - 38 x - 14

Find intervals:

Increasing

: - \infty < x < \frac{- 1621 + 19}{90},

Decreasing

: \frac{- 1621 + 19}{90} < x < \frac{1621 + 19}{90},

Increasing

: \frac{1621 + 19}{90} < x < \infty

Plug

x = \frac{19 - 1621}{90}

into

30 x^{3} - 19 x^{2} - 14 x + 8 : \frac{1621 1621 - 42769}{12150} + 8

Maximum (\frac{19 - 1621}{90}, \frac{1621 1621 - 42769}{12150} + 8)

Plug

x = \frac{19 + 1621}{90}

into

30 x^{3} - 19 x^{2} - 14 x + 8 : \frac{- 42769 - 1621 1621}{12150} + 8

Minimum (\frac{19 + 1621}{90}, \frac{- 42769 - 1621 1621}{12150} + 8)

Maximum (\frac{19 - 1621}{90}, \frac{1621 1621 - 42769}{12150} + 8), Minimum (\frac{19 + 1621}{90}, \frac{- 42769 - 1621 1621}{12150} + 8)

Graph

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Frequently Asked Questions (FAQ)

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