What is the extreme f(x)=2x(x-1)^2 ?

The extreme f(x)=2x(x-1)^2 is Maximum(1/3 , 8/27),Minimum(1,0)

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extreme f(x)=2x(x-1)^2

extreme points

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

Maximum (\frac{1}{3}, \frac{8}{27}), Minimum (1, 0)

Solution steps

f^{'} (x) = 2 (3 x^{2} - 4 x + 1)

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 (x - 1)^{2} : \frac{8}{27}

Maximum (\frac{1}{3}, \frac{8}{27})

Plug

x = 1

into

2 x (x - 1)^{2} : 0

Minimum (1, 0)

Maximum (\frac{1}{3}, \frac{8}{27}), Minimum (1, 0)

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

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

6 x^{5} - 10 x^{3}

f (x, y) = 2 x^{3} + 4 x y - y^{2}

f (x, y) = x^{3} + y^{3} - 36 x y

What is the extreme f(x)=2x(x-1)^2 ?
The extreme f(x)=2x(x-1)^2 is Maximum(1/3 , 8/27),Minimum(1,0)