What is the extreme x^3-8x^2-12x+8 ?

The extreme x^3-8x^2-12x+8 is Maximum(-2/3 , 328/27),Minimum(6,-136)

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extreme x^3-8x^2-12x+8

extreme points

x^{3} - 8 x^{2} - 12 x + 8

Maximum (- \frac{2}{3}, \frac{328}{27}), Minimum (6, - 136)

Solution steps

f^{'} (x) = 3 x^{2} - 16 x - 12

Find intervals:

Increasing

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

Decreasing

: - \frac{2}{3} < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} - 8 x^{2} - 12 x + 8 : \frac{328}{27}

Maximum (- \frac{2}{3}, \frac{328}{27})

Plug

x = 6

into

x^{3} - 8 x^{2} - 12 x + 8 : - 136

Minimum (6, - 136)

Maximum (- \frac{2}{3}, \frac{328}{27}), Minimum (6, - 136)

(x, - 2), (- 1, 4)

f (x) = - 6 x^{4}

\frac{x ^{2} - 3}{x + 3}

(3, 4), (- 2, 1)

f (x) = (x + 5)^{3} - 2

What is the extreme x^3-8x^2-12x+8 ?
The extreme x^3-8x^2-12x+8 is Maximum(-2/3 , 328/27),Minimum(6,-136)