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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282), Minimum (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

Solution steps

f^{'} (x) = 3 x^{2} + 16 x - 6

Find intervals:

Increasing

: - \infty < x < \frac{- 82 - 8}{3},

Decreasing

: \frac{- 82 - 8}{3} < x < \frac{82 - 8}{3},

Increasing

: \frac{82 - 8}{3} < x < \infty

Plug

x = - \frac{8 + 82}{3}

into

x^{3} + 8 x^{2} - 6 x - 4 : \frac{1024 + 110 82}{27} + 12 + 282

Maximum (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282)

Plug

x = \frac{- 8 + 82}{3}

into

x^{3} + 8 x^{2} - 6 x - 4 : \frac{1024 - 110 82}{27} + 12 - 282

Minimum (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

Maximum (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282), Minimum (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

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Frequently Asked Questions (FAQ)

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