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Popular Functions >

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

Solution

extreme points

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

Solution

Minimum (0, - 3), Maximum (\frac{15 - 65}{8}, \frac{25 ( 13 65 - 83 )}{512} - 3), Minimum (\frac{15 + 65}{8}, - \frac{25 ( 83 + 13 65 )}{512} - 3)

Solution steps

f^{'} (x) = 4 x^{3} - 15 x^{2} + 10 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{15 - 65}{8},

Decreasing

: \frac{15 - 65}{8} < x < \frac{15 + 65}{8},

Increasing

: \frac{15 + 65}{8} < x < \infty

Plug

x = 0

into

x^{4} - 5 x^{3} + 5 x^{2} - 3 : - 3

Minimum (0, - 3)

Plug

x = \frac{15 - 65}{8}

into

x^{4} - 5 x^{3} + 5 x^{2} - 3 : \frac{25 ( 13 65 - 83 )}{512} - 3

Maximum (\frac{15 - 65}{8}, \frac{25 ( 13 65 - 83 )}{512} - 3)

Plug

x = \frac{15 + 65}{8}

into

x^{4} - 5 x^{3} + 5 x^{2} - 3 : - \frac{25 ( 83 + 13 65 )}{512} - 3

Minimum (\frac{15 + 65}{8}, - \frac{25 ( 83 + 13 65 )}{512} - 3)

Minimum (0, - 3), Maximum (\frac{15 - 65}{8}, \frac{25 ( 13 65 - 83 )}{512} - 3), Minimum (\frac{15 + 65}{8}, - \frac{25 ( 83 + 13 65 )}{512} - 3)

Graph

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Frequently Asked Questions (FAQ)

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