What is the extreme 2x^3-4x^2+2x+1 ?

The extreme 2x^3-4x^2+2x+1 is Maximum(1/3 , 35/27),Minimum(1,1)

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extreme 2x^3-4x^2+2x+1

extreme points

2 x^{3} - 4 x^{2} + 2 x + 1

Maximum (\frac{1}{3}, \frac{35}{27}), Minimum (1, 1)

Solution steps

f^{'} (x) = 6 x^{2} - 8 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} - 4 x^{2} + 2 x + 1 : \frac{35}{27}

Maximum (\frac{1}{3}, \frac{35}{27})

Plug

x = 1

into

2 x^{3} - 4 x^{2} + 2 x + 1 : 1

Minimum (1, 1)

Maximum (\frac{1}{3}, \frac{35}{27}), Minimum (1, 1)

y (x, t) = x (3 t)

f (x) = 3 x^{\frac{2}{3}} - 2 x [- 1.1]

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

f (x, y) = \frac{1}{3} 36 - 4 x^{2} - 9 y^{2}

f (x) = 0.2 (x^{4} + 4 x^{3} - 16 x - 16) + 5

What is the extreme 2x^3-4x^2+2x+1 ?
The extreme 2x^3-4x^2+2x+1 is Maximum(1/3 , 35/27),Minimum(1,1)