What is the extreme f(x)=x^3-x^2,0<= x<= 5 ?

The extreme f(x)=x^3-x^2,0<= x<= 5 is Maximum(0,0),Minimum(2/3 ,-4/27),Maximum(5,100)

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extreme f(x)=x^3-x^2,0<= x<= 5

extreme points

f (x) = x^{3} - x^{2}, 0 \leq x \leq 5

Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{4}{27}), Maximum (5, 100)

Solution steps

Find the critical points:

x = 0, x = \frac{2}{3}, x = 5

Domain of

x^{3} - x^{2}, 0 \leq x \leq 5 : 0 \leq x \leq 5

Find intervals:

Decreasing

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

Increasing

: \frac{2}{3} < x < 5

Plug the extreme point

x = 0

into

x^{3} - x^{2} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = \frac{2}{3}

into

x^{3} - x^{2} \Rightarrow y = - \frac{4}{27}

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

Plug the extreme point

x = 5

into

x^{3} - x^{2} \Rightarrow y = 100

Maximum (5, 100)

Maximum (0, 0), Minimum (\frac{2}{3}, - \frac{4}{27}), Maximum (5, 100)

f (x, y) = 72 x^{4} + y^{2} - 24 x y

f (x) = x^{3} + y^{3} - 18 x y

f (x) = x^{3} - 6 x^{2} + 9 x - 1

f (x) = x^{3} - 6 x^{2} + 9 x - 4

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

What is the extreme f(x)=x^3-x^2,0<= x<= 5 ?
The extreme f(x)=x^3-x^2,0<= x<= 5 is Maximum(0,0),Minimum(2/3 ,-4/27),Maximum(5,100)