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

The extreme f(x)=x^3-3x^2-1 is Maximum(0,-1),Minimum(2,-5)

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

extreme

Maximum (0, - 1), Minimum (2, - 5)

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 : - 5

Minimum (2, - 5)

Maximum (0, - 1), Minimum (2, - 5)

What is the extreme f(x)=x^3-3x^2-1 ?
The extreme f(x)=x^3-3x^2-1 is Maximum(0,-1),Minimum(2,-5)