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Popular >

extreme f(x)=(x^3)/3+8x^2-18x+7

Solution

extreme points

f (x) = \frac{x ^{3}}{3} + 8 x^{2} - 18 x + 7

Solution

Maximum (- 8 - 82, \frac{- 2480 - 274 82}{3} + 1319 + 14682), Minimum (- 8 + 82, \frac{274 82 - 2480}{3} + 1319 - 14682)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 82 - 8,

Decreasing

: - 82 - 8 < x < 82 - 8,

Increasing

: 82 - 8 < x < \infty

Plug

x = - 8 - 82

into

\frac{x ^{3}}{3} + 8 x^{2} - 18 x + 7 : \frac{- 2480 - 274 82}{3} + 1319 + 14682

Maximum (- 8 - 82, \frac{- 2480 - 274 82}{3} + 1319 + 14682)

Plug

x = - 8 + 82

into

\frac{x ^{3}}{3} + 8 x^{2} - 18 x + 7 : \frac{274 82 - 2480}{3} + 1319 - 14682

Minimum (- 8 + 82, \frac{274 82 - 2480}{3} + 1319 - 14682)

Maximum (- 8 - 82, \frac{- 2480 - 274 82}{3} + 1319 + 14682), Minimum (- 8 + 82, \frac{274 82 - 2480}{3} + 1319 - 14682)

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Frequently Asked Questions (FAQ)

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