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Popular Functions >

extreme f(x)=x^4-7x^3-13x^2

Solution

extreme

Solution

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512}), Maximum (0, 0), Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Solution steps

f^{'} (x) = 4 x^{3} - 21 x^{2} - 26 x

Find intervals:

Decreasing

: - \infty < x < \frac{21 - 857}{8},

Increasing

: \frac{21 - 857}{8} < x < 0,

Decreasing

: 0 < x < \frac{21 + 857}{8},

Increasing

: \frac{21 + 857}{8} < x < \infty

Plug

x = \frac{21 - 857}{8}

into

x^{4} - 7 x^{3} - 13 x^{2} : \frac{5999 857 - 178187}{512}

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512})

Plug

x = 0

into

x^{4} - 7 x^{3} - 13 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{21 + 857}{8}

into

x^{4} - 7 x^{3} - 13 x^{2} : - \frac{178187 + 5999 857}{512}

Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512}), Maximum (0, 0), Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Graph

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Frequently Asked Questions (FAQ)

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