What is the extreme f(x)=2x^3-2x^2-2x+6 ?

The extreme f(x)=2x^3-2x^2-2x+6 is Maximum(-1/3 , 172/27),Minimum(1,4)

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extreme f(x)=2x^3-2x^2-2x+6

extreme points

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

Maximum (- \frac{1}{3}, \frac{172}{27}), Minimum (1, 4)

Solution steps

f^{'} (x) = 6 x^{2} - 4 x - 2

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

2 x^{3} - 2 x^{2} - 2 x + 6 : \frac{172}{27}

Maximum (- \frac{1}{3}, \frac{172}{27})

Plug

x = 1

into

2 x^{3} - 2 x^{2} - 2 x + 6 : 4

Minimum (1, 4)

Maximum (- \frac{1}{3}, \frac{172}{27}), Minimum (1, 4)

f (x) = (4 x^{2} - 64)^{\frac{1}{5}}

f (x, y) = e^{y^{2} + x^{3} - 6 x y - 6 x + 2 y}

\frac{2 x + 4}{x ^{2} - 16}

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

f (x) = x [18 - 2 (x)]^{2}

What is the extreme f(x)=2x^3-2x^2-2x+6 ?
The extreme f(x)=2x^3-2x^2-2x+6 is Maximum(-1/3 , 172/27),Minimum(1,4)