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Popular >

extreme f(x)=-8x^3+110x^2-143x+590

Solution

extreme points

f (x) = - 8 x^{3} + 110 x^{2} - 143 x + 590

Solution

Minimum (\frac{55 - 2167}{12}, \frac{95590 - 2167 2167}{108} + 590), Maximum (\frac{55 + 2167}{12}, \frac{95590 + 2167 2167}{108} + 590)

Solution steps

f^{'} (x) = - 24 x^{2} + 220 x - 143

Find intervals:

Decreasing

: - \infty < x < \frac{- 2167 + 55}{12},

Increasing

: \frac{- 2167 + 55}{12} < x < \frac{2167 + 55}{12},

Decreasing

: \frac{2167 + 55}{12} < x < \infty

Plug

x = \frac{55 - 2167}{12}

into

- 8 x^{3} + 110 x^{2} - 143 x + 590 : \frac{95590 - 2167 2167}{108} + 590

Minimum (\frac{55 - 2167}{12}, \frac{95590 - 2167 2167}{108} + 590)

Plug

x = \frac{55 + 2167}{12}

into

- 8 x^{3} + 110 x^{2} - 143 x + 590 : \frac{95590 + 2167 2167}{108} + 590

Maximum (\frac{55 + 2167}{12}, \frac{95590 + 2167 2167}{108} + 590)

Minimum (\frac{55 - 2167}{12}, \frac{95590 - 2167 2167}{108} + 590), Maximum (\frac{55 + 2167}{12}, \frac{95590 + 2167 2167}{108} + 590)

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extreme y=-2x^2+12x-8 extreme points

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Frequently Asked Questions (FAQ)

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