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Popular >

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

Solution

extreme points

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

Solution

Maximum (\frac{6 - 30}{3}, \frac{288 - 52 30}{9} + 830 - 46), Minimum (\frac{6 + 30}{3}, \frac{288 + 52 30}{9} - 46 - 830)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x + 2

Find intervals:

Increasing

: - \infty < x < - \frac{10}{3} + 2,

Decreasing

: - \frac{10}{3} + 2 < x < \frac{10}{3} + 2,

Increasing

: \frac{10}{3} + 2 < x < \infty

Plug

x = \frac{6 - 30}{3}

into

x^{3} - 6 x^{2} + 2 x - 2 : \frac{288 - 52 30}{9} + 830 - 46

Maximum (\frac{6 - 30}{3}, \frac{288 - 52 30}{9} + 830 - 46)

Plug

x = \frac{6 + 30}{3}

into

x^{3} - 6 x^{2} + 2 x - 2 : \frac{288 + 52 30}{9} - 46 - 830

Minimum (\frac{6 + 30}{3}, \frac{288 + 52 30}{9} - 46 - 830)

Maximum (\frac{6 - 30}{3}, \frac{288 - 52 30}{9} + 830 - 46), Minimum (\frac{6 + 30}{3}, \frac{288 + 52 30}{9} - 46 - 830)

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