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Popular >

extreme f(x)=x^3+18x^2+11x-16

Solution

extreme points

f (x) = x^{3} + 18 x^{2} + 11 x - 16

Solution

Maximum (- \frac{18 + 291}{3}, \frac{- 7776 - 454 291}{9} + 1214 + 72291), Minimum (\frac{- 18 + 291}{3}, \frac{454 291 - 7776}{9} + 1214 - 72291)

Solution steps

f^{'} (x) = 3 x^{2} + 36 x + 11

Find intervals:

Increasing

: - \infty < x < - \frac{97}{3} - 6,

Decreasing

: - \frac{97}{3} - 6 < x < \frac{97}{3} - 6,

Increasing

: \frac{97}{3} - 6 < x < \infty

Plug

x = - \frac{18 + 291}{3}

into

x^{3} + 18 x^{2} + 11 x - 16 : \frac{- 7776 - 454 291}{9} + 1214 + 72291

Maximum (- \frac{18 + 291}{3}, \frac{- 7776 - 454 291}{9} + 1214 + 72291)

Plug

x = \frac{- 18 + 291}{3}

into

x^{3} + 18 x^{2} + 11 x - 16 : \frac{454 291 - 7776}{9} + 1214 - 72291

Minimum (\frac{- 18 + 291}{3}, \frac{454 291 - 7776}{9} + 1214 - 72291)

Maximum (- \frac{18 + 291}{3}, \frac{- 7776 - 454 291}{9} + 1214 + 72291), Minimum (\frac{- 18 + 291}{3}, \frac{454 291 - 7776}{9} + 1214 - 72291)

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Frequently Asked Questions (FAQ)

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