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

The extreme x^3-2x^2-4x-4 is Maximum(-2/3 ,-68/27),Minimum(2,-12)

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

extreme points

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

Maximum (- \frac{2}{3}, - \frac{68}{27}), Minimum (2, - 12)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 2 < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} - 2 x^{2} - 4 x - 4 : - \frac{68}{27}

Maximum (- \frac{2}{3}, - \frac{68}{27})

Plug

x = 2

into

x^{3} - 2 x^{2} - 4 x - 4 : - 12

Minimum (2, - 12)

Maximum (- \frac{2}{3}, - \frac{68}{27}), Minimum (2, - 12)

9 x^{3} - 7 x^{2} + 3 x + 10

f (x) = 4 + 27 x - x^{3}

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

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

y = x^{2} - 4 x + 19

What is the extreme x^3-2x^2-4x-4 ?
The extreme x^3-2x^2-4x-4 is Maximum(-2/3 ,-68/27),Minimum(2,-12)