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Popular >

extreme f(x)=x^4-5x^3-15x^2

Solution

extreme points

f (x) = x^{4} - 5 x^{3} - 15 x^{2}

Solution

Minimum (\frac{15 - 705}{8}, \frac{75 ( 47 705 - 1329 )}{512}), Maximum (0, 0), Minimum (\frac{15 + 705}{8}, - \frac{75 ( 1329 + 47 705 )}{512})

Solution steps

f^{'} (x) = 4 x^{3} - 15 x^{2} - 30 x

Find intervals:

Decreasing

: - \infty < x < \frac{15 - 705}{8},

Increasing

: \frac{15 - 705}{8} < x < 0,

Decreasing

: 0 < x < \frac{15 + 705}{8},

Increasing

: \frac{15 + 705}{8} < x < \infty

Plug

x = \frac{15 - 705}{8}

into

x^{4} - 5 x^{3} - 15 x^{2} : \frac{75 ( 47 705 - 1329 )}{512}

Minimum (\frac{15 - 705}{8}, \frac{75 ( 47 705 - 1329 )}{512})

Plug

x = 0

into

x^{4} - 5 x^{3} - 15 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{15 + 705}{8}

into

x^{4} - 5 x^{3} - 15 x^{2} : - \frac{75 ( 1329 + 47 705 )}{512}

Minimum (\frac{15 + 705}{8}, - \frac{75 ( 1329 + 47 705 )}{512})

Minimum (\frac{15 - 705}{8}, \frac{75 ( 47 705 - 1329 )}{512}), Maximum (0, 0), Minimum (\frac{15 + 705}{8}, - \frac{75 ( 1329 + 47 705 )}{512})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^4-5x^3-15x^2 ?
The extreme f(x)=x^4-5x^3-15x^2 is