What is the extreme f(x)=-6x^2+2x^3 ?

The extreme f(x)=-6x^2+2x^3 is Maximum(0,0),Minimum(2,-8)

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extreme f(x)=-6x^2+2x^3

extreme

Maximum (0, 0), Minimum (2, - 8)

Solution steps

f^{'} (x) = - 12 x + 6 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

- 6 x^{2} + 2 x^{3} : 0

Maximum (0, 0)

Plug

x = 2

into

- 6 x^{2} + 2 x^{3} : - 8

Minimum (2, - 8)

Maximum (0, 0), Minimum (2, - 8)

What is the extreme f(x)=-6x^2+2x^3 ?
The extreme f(x)=-6x^2+2x^3 is Maximum(0,0),Minimum(2,-8)