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Popular Functions >

extreme f(x)=x^3+3x^2-4x-12

Solution

extreme

Solution

Maximum (- \frac{3 + 21}{3}, \frac{- 36 - 4 21}{9} + 221 - 2), Minimum (\frac{- 3 + 21}{3}, \frac{4 21 - 36}{9} - 2 - 221)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3} - 1,

Decreasing

: - \frac{7}{3} - 1 < x < \frac{7}{3} - 1,

Increasing

: \frac{7}{3} - 1 < x < \infty

Plug

x = - \frac{3 + 21}{3}

into

x^{3} + 3 x^{2} - 4 x - 12 : \frac{- 36 - 4 21}{9} + 221 - 2

Maximum (- \frac{3 + 21}{3}, \frac{- 36 - 4 21}{9} + 221 - 2)

Plug

x = \frac{- 3 + 21}{3}

into

x^{3} + 3 x^{2} - 4 x - 12 : \frac{4 21 - 36}{9} - 2 - 221

Minimum (\frac{- 3 + 21}{3}, \frac{4 21 - 36}{9} - 2 - 221)

Maximum (- \frac{3 + 21}{3}, \frac{- 36 - 4 21}{9} + 221 - 2), Minimum (\frac{- 3 + 21}{3}, \frac{4 21 - 36}{9} - 2 - 221)

Graph

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Frequently Asked Questions (FAQ)

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