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Popular >

extreme f(x)=4x^3-3x^2-72x-80

Solution

extreme points

f (x) = 4 x^{3} - 3 x^{2} - 72 x - 80

Solution

Maximum (\frac{1 - 97}{4}, \frac{- 1 - 47 97}{8} + 1897 - 98), Minimum (\frac{1 + 97}{4}, \frac{47 97 - 1}{8} - 98 - 1897)

Solution steps

f^{'} (x) = 12 x^{2} - 6 x - 72

Find intervals:

Increasing

: - \infty < x < \frac{- 97 + 1}{4},

Decreasing

: \frac{- 97 + 1}{4} < x < \frac{97 + 1}{4},

Increasing

: \frac{97 + 1}{4} < x < \infty

Plug

x = \frac{1 - 97}{4}

into

4 x^{3} - 3 x^{2} - 72 x - 80 : \frac{- 1 - 47 97}{8} + 1897 - 98

Maximum (\frac{1 - 97}{4}, \frac{- 1 - 47 97}{8} + 1897 - 98)

Plug

x = \frac{1 + 97}{4}

into

4 x^{3} - 3 x^{2} - 72 x - 80 : \frac{47 97 - 1}{8} - 98 - 1897

Minimum (\frac{1 + 97}{4}, \frac{47 97 - 1}{8} - 98 - 1897)

Maximum (\frac{1 - 97}{4}, \frac{- 1 - 47 97}{8} + 1897 - 98), Minimum (\frac{1 + 97}{4}, \frac{47 97 - 1}{8} - 98 - 1897)

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extreme f(x)=-2x^3+42x^2-270x+3 extreme points

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extreme f(x)=-2x^3+42x^2-270x+8 extreme points

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Frequently Asked Questions (FAQ)

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