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Popular Functions >

extreme f(x)=-x^3+6x^2-10x+4

Solution

extreme points

f (x) = - x^{3} + 6 x^{2} - 10 x + 4

Solution

Minimum (\frac{6 - 6}{3}, \frac{68 2 - 96 3}{3 3} + 32 - 86), Maximum (\frac{6 + 6}{3}, \frac{- 96 3 - 68 2}{3 3} + 32 + 86)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x - 10

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

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

into

- x^{3} + 6 x^{2} - 10 x + 4 : \frac{68 2 - 96 3}{3 3} + 32 - 86

Minimum (\frac{6 - 6}{3}, \frac{68 2 - 96 3}{3 3} + 32 - 86)

Plug

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

into

- x^{3} + 6 x^{2} - 10 x + 4 : \frac{- 96 3 - 68 2}{3 3} + 32 + 86

Maximum (\frac{6 + 6}{3}, \frac{- 96 3 - 68 2}{3 3} + 32 + 86)

Minimum (\frac{6 - 6}{3}, \frac{68 2 - 96 3}{3 3} + 32 - 86), Maximum (\frac{6 + 6}{3}, \frac{- 96 3 - 68 2}{3 3} + 32 + 86)

Graph

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