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Popular >

extreme f(x)=x^4-4x^3-18x^2

Solution

extreme points

f (x) = x^{4} - 4 x^{3} - 18 x^{2}

Solution

Minimum (\frac{3 - 3 5}{2}, \frac{( 3 - 3 5 ) ^{4}}{16} + 1895 - 459), Maximum (0, 0), Minimum (\frac{3 + 3 5}{2}, \frac{( 3 + 3 5 ) ^{4}}{16} - 459 - 1895)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2} - 36 x

Find intervals:

Decreasing

: - \infty < x < \frac{3 - 3 5}{2},

Increasing

: \frac{3 - 3 5}{2} < x < 0,

Decreasing

: 0 < x < \frac{3 + 3 5}{2},

Increasing

: \frac{3 + 3 5}{2} < x < \infty

Plug

x = \frac{3 - 3 5}{2}

into

x^{4} - 4 x^{3} - 18 x^{2} : \frac{( 3 - 3 5 ) ^{4}}{16} + 1895 - 459

Minimum (\frac{3 - 3 5}{2}, \frac{( 3 - 3 5 ) ^{4}}{16} + 1895 - 459)

Plug

x = 0

into

x^{4} - 4 x^{3} - 18 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{3 + 3 5}{2}

into

x^{4} - 4 x^{3} - 18 x^{2} : \frac{( 3 + 3 5 ) ^{4}}{16} - 459 - 1895

Minimum (\frac{3 + 3 5}{2}, \frac{( 3 + 3 5 ) ^{4}}{16} - 459 - 1895)

Minimum (\frac{3 - 3 5}{2}, \frac{( 3 - 3 5 ) ^{4}}{16} + 1895 - 459), Maximum (0, 0), Minimum (\frac{3 + 3 5}{2}, \frac{( 3 + 3 5 ) ^{4}}{16} - 459 - 1895)

Graph

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Frequently Asked Questions (FAQ)

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