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Popular >

extreme x^4-8x^3+7x^2+6x-4

Solution

extreme points

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4

Solution

Minimum (\frac{5 - 31}{2}, \frac{1951 - 350 31}{4} + 10331 - 579), Maximum (1, 2), Minimum (\frac{5 + 31}{2}, \frac{1951 + 350 31}{4} - 579 - 10331)

Solution steps

f^{'} (x) = 4 x^{3} - 24 x^{2} + 14 x + 6

Find intervals:

Decreasing

: - \infty < x < \frac{5 - 31}{2},

Increasing

: \frac{5 - 31}{2} < x < 1,

Decreasing

: 1 < x < \frac{5 + 31}{2},

Increasing

: \frac{5 + 31}{2} < x < \infty

Plug

x = \frac{5 - 31}{2}

into

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4 : \frac{1951 - 350 31}{4} + 10331 - 579

Minimum (\frac{5 - 31}{2}, \frac{1951 - 350 31}{4} + 10331 - 579)

Plug

x = 1

into

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4 : 2

Maximum (1, 2)

Plug

x = \frac{5 + 31}{2}

into

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4 : \frac{1951 + 350 31}{4} - 579 - 10331

Minimum (\frac{5 + 31}{2}, \frac{1951 + 350 31}{4} - 579 - 10331)

Minimum (\frac{5 - 31}{2}, \frac{1951 - 350 31}{4} + 10331 - 579), Maximum (1, 2), Minimum (\frac{5 + 31}{2}, \frac{1951 + 350 31}{4} - 579 - 10331)

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Frequently Asked Questions (FAQ)

What is the extreme x^4-8x^3+7x^2+6x-4 ?
The extreme x^4-8x^3+7x^2+6x-4 is