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

The extreme 3x^3-3x^2-3x+8 is Maximum(-1/3 , 77/9),Minimum(1,5)

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

extreme points

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

Maximum (- \frac{1}{3}, \frac{77}{9}), Minimum (1, 5)

Solution steps

f^{'} (x) = 9 x^{2} - 6 x - 3

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

3 x^{3} - 3 x^{2} - 3 x + 8 : \frac{77}{9}

Maximum (- \frac{1}{3}, \frac{77}{9})

Plug

x = 1

into

3 x^{3} - 3 x^{2} - 3 x + 8 : 5

Minimum (1, 5)

Maximum (- \frac{1}{3}, \frac{77}{9}), Minimum (1, 5)

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

f (x) = x^{2} - 2 x - 6

f (x) = x^{2} - 2 x - 1

f (x) = x y + \frac{8}{x} + \frac{8}{y}

f (x, y) = ln (x y - 1)

What is the extreme 3x^3-3x^2-3x+8 ?
The extreme 3x^3-3x^2-3x+8 is Maximum(-1/3 , 77/9),Minimum(1,5)