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

The extreme g(x)=x^3-3x^2+1 is Maximum(0,1),Minimum(2,-3)

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

extreme

Maximum (0, 1), Minimum (2, - 3)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Maximum (0, 1)

Plug

x = 2

into

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

Minimum (2, - 3)

Maximum (0, 1), Minimum (2, - 3)

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