What is the extreme x^3+2x^2-4x+2 ?

The extreme x^3+2x^2-4x+2 is Maximum(-2,10),Minimum(2/3 , 14/27)

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extreme x^3+2x^2-4x+2

extreme points

x^{3} + 2 x^{2} - 4 x + 2

Maximum (- 2, 10), Minimum (\frac{2}{3}, \frac{14}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

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

Increasing

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

Plug

x = - 2

into

x^{3} + 2 x^{2} - 4 x + 2 : 10

Maximum (- 2, 10)

Plug

x = \frac{2}{3}

into

x^{3} + 2 x^{2} - 4 x + 2 : \frac{14}{27}

Minimum (\frac{2}{3}, \frac{14}{27})

Maximum (- 2, 10), Minimum (\frac{2}{3}, \frac{14}{27})

x^{3} + 2 x^{2} - 4 x + 8

f (x) = x^{3} - x^{2} - 8 x + 2

f (x) = x^{3} - x^{2} - 8 x + 1

f (x) = (x + 1)^{\frac{2}{3}}

y = \frac{x ^{2} + 10 x + 9}{x ^{2} + 2 x + 1}

What is the extreme x^3+2x^2-4x+2 ?
The extreme x^3+2x^2-4x+2 is Maximum(-2,10),Minimum(2/3 , 14/27)