What is the extreme f(x)=x^3-8x^2-12x+9 ?

The extreme f(x)=x^3-8x^2-12x+9 is Maximum(-2/3 , 355/27),Minimum(6,-135)

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extreme f(x)=x^3-8x^2-12x+9

extreme

Maximum (- \frac{2}{3}, \frac{355}{27}), Minimum (6, - 135)

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 + 9 : \frac{355}{27}

Maximum (- \frac{2}{3}, \frac{355}{27})

Plug

x = 6

into

x^{3} - 8 x^{2} - 12 x + 9 : - 135

Minimum (6, - 135)

Maximum (- \frac{2}{3}, \frac{355}{27}), Minimum (6, - 135)

What is the extreme f(x)=x^3-8x^2-12x+9 ?
The extreme f(x)=x^3-8x^2-12x+9 is Maximum(-2/3 , 355/27),Minimum(6,-135)