What is the extreme f(x)=x^3-30x^2,(-10,30) ?

The extreme f(x)=x^3-30x^2,(-10,30) is Maximum(0,0),Minimum(20,-4000)

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extreme f(x)=x^3-30x^2,(-10,30)

extreme

Maximum (0, 0), Minimum (20, - 4000)

Solution steps

Find the critical points:

x = 0, x = 20

Domain of

x^{3} - 30 x^{2}, (- 10, 30) : - 10 < x < 30

Find intervals:

Increasing

: - 10 < x < 0,

Decreasing

: 0 < x < 20,

Increasing

: 20 < x < 30

Plug the extreme point

x = 0

into

x^{3} - 30 x^{2} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 20

into

x^{3} - 30 x^{2} \Rightarrow y = - 4000

Minimum (20, - 4000)

Maximum (0, 0), Minimum (20, - 4000)

What is the extreme f(x)=x^3-30x^2,(-10,30) ?
The extreme f(x)=x^3-30x^2,(-10,30) is Maximum(0,0),Minimum(20,-4000)