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Popular >

extreme x^4-x^3-6x^2

Solution

extreme points

x^{4} - x^{3} - 6 x^{2}

Solution

Minimum (\frac{3 - 201}{8}, \frac{3 ( 67 201 - 1833 )}{512}), Maximum (0, 0), Minimum (\frac{3 + 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512})

Solution steps

f^{'} (x) = 4 x^{3} - 3 x^{2} - 12 x

Find intervals:

Decreasing

: - \infty < x < \frac{3 - 201}{8},

Increasing

: \frac{3 - 201}{8} < x < 0,

Decreasing

: 0 < x < \frac{3 + 201}{8},

Increasing

: \frac{3 + 201}{8} < x < \infty

Plug

x = \frac{3 - 201}{8}

into

x^{4} - x^{3} - 6 x^{2} : \frac{3 ( 67 201 - 1833 )}{512}

Minimum (\frac{3 - 201}{8}, \frac{3 ( 67 201 - 1833 )}{512})

Plug

x = 0

into

x^{4} - x^{3} - 6 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{3 + 201}{8}

into

x^{4} - x^{3} - 6 x^{2} : - \frac{3 ( 1833 + 67 201 )}{512}

Minimum (\frac{3 + 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512})

Minimum (\frac{3 - 201}{8}, \frac{3 ( 67 201 - 1833 )}{512}), Maximum (0, 0), Minimum (\frac{3 + 201}{8}, - \frac{3 ( 1833 + 67 201 )}{512})

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Frequently Asked Questions (FAQ)

What is the extreme x^4-x^3-6x^2 ?
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