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Popular >

extreme f(x)=60x^4-60x^3-60x^2

Solution

extreme points

f (x) = 60 x^{4} - 60 x^{3} - 60 x^{2}

Solution

Minimum (\frac{3 - 41}{8}, \frac{15 ( 41 41 - 299 )}{128}), Maximum (0, 0), Minimum (\frac{3 + 41}{8}, - \frac{15 ( 299 + 41 41 )}{128})

Solution steps

f^{'} (x) = 240 x^{3} - 180 x^{2} - 120 x

Find intervals:

Decreasing

: - \infty < x < \frac{3 - 41}{8},

Increasing

: \frac{3 - 41}{8} < x < 0,

Decreasing

: 0 < x < \frac{3 + 41}{8},

Increasing

: \frac{3 + 41}{8} < x < \infty

Plug

x = \frac{3 - 41}{8}

into

60 x^{4} - 60 x^{3} - 60 x^{2} : \frac{15 ( 41 41 - 299 )}{128}

Minimum (\frac{3 - 41}{8}, \frac{15 ( 41 41 - 299 )}{128})

Plug

x = 0

into

60 x^{4} - 60 x^{3} - 60 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{3 + 41}{8}

into

60 x^{4} - 60 x^{3} - 60 x^{2} : - \frac{15 ( 299 + 41 41 )}{128}

Minimum (\frac{3 + 41}{8}, - \frac{15 ( 299 + 41 41 )}{128})

Minimum (\frac{3 - 41}{8}, \frac{15 ( 41 41 - 299 )}{128}), Maximum (0, 0), Minimum (\frac{3 + 41}{8}, - \frac{15 ( 299 + 41 41 )}{128})

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Frequently Asked Questions (FAQ)

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