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

The extreme f(x)=2x^3-x^2+2 is Maximum(0,2),Minimum(1/3 , 53/27)

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

extreme points

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

Maximum (0, 2), Minimum (\frac{1}{3}, \frac{53}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

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

Maximum (0, 2)

Plug

x = \frac{1}{3}

into

2 x^{3} - x^{2} + 2 : \frac{53}{27}

Minimum (\frac{1}{3}, \frac{53}{27})

Maximum (0, 2), Minimum (\frac{1}{3}, \frac{53}{27})

y = 2 x^{3} - 9 x

f (x) = 12 x^{2} - 24 x

f (x) = \frac{5 ( x + 4 )}{x ^{2} + x - 12}

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

f (x) = x

What is the extreme f(x)=2x^3-x^2+2 ?
The extreme f(x)=2x^3-x^2+2 is Maximum(0,2),Minimum(1/3 , 53/27)