What is the extreme f(x)=x^3-x^2+1 ?

The extreme f(x)=x^3-x^2+1 is Maximum(0,1),Minimum(2/3 ,-4/27+1)

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extreme f(x)=x^3-x^2+1

extreme points

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

Maximum (0, 1), Minimum (\frac{2}{3}, - \frac{4}{27} + 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{2}{3},

Increasing

: \frac{2}{3} < x < \infty

Plug

x = 0

into

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

Maximum (0, 1)

Plug

x = \frac{2}{3}

into

x^{3} - x^{2} + 1 : - \frac{4}{27} + 1

Minimum (\frac{2}{3}, - \frac{4}{27} + 1)

Maximum (0, 1), Minimum (\frac{2}{3}, - \frac{4}{27} + 1)

f (x) = 13 x + 4

f (x) = x^{2} + 10 x + 24

f (x) = \frac{x}{8 - 9 x}

f (x) = \frac{x - 1}{x ^{2} - 5 x + 6}

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

What is the extreme f(x)=x^3-x^2+1 ?
The extreme f(x)=x^3-x^2+1 is Maximum(0,1),Minimum(2/3 ,-4/27+1)