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Popular >

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

Solution

extreme points

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

Solution

Maximum (- 1, 0), Minimum (\frac{11 - 3 17}{16}, \frac{16859 - 4131 17}{4096} - 2), Maximum (\frac{11 + 3 17}{16}, \frac{16859 + 4131 17}{4096} - 2)

Solution steps

f^{'} (x) = - 8 x^{3} + 3 x^{2} + 12 x + 1

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{11 - 3 17}{16},

Increasing

: \frac{11 - 3 17}{16} < x < \frac{11 + 3 17}{16},

Decreasing

: \frac{11 + 3 17}{16} < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 0)

Plug

x = \frac{11 - 3 17}{16}

into

- 2 x^{4} + x^{3} + 6 x^{2} + x - 2 : \frac{16859 - 4131 17}{4096} - 2

Minimum (\frac{11 - 3 17}{16}, \frac{16859 - 4131 17}{4096} - 2)

Plug

x = \frac{11 + 3 17}{16}

into

- 2 x^{4} + x^{3} + 6 x^{2} + x - 2 : \frac{16859 + 4131 17}{4096} - 2

Maximum (\frac{11 + 3 17}{16}, \frac{16859 + 4131 17}{4096} - 2)

Maximum (- 1, 0), Minimum (\frac{11 - 3 17}{16}, \frac{16859 - 4131 17}{4096} - 2), Maximum (\frac{11 + 3 17}{16}, \frac{16859 + 4131 17}{4096} - 2)

Popular Examples

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Frequently Asked Questions (FAQ)

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