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

The extreme f(x)=-x^3+6x^2-2 is Minimum(0,-2),Maximum(4,30)

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

extreme points

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

Minimum (0, - 2), Maximum (4, 30)

Solution steps

f^{'} (x) = - 3 x^{2} + 12 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

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

Minimum (0, - 2)

Plug

x = 4

into

- x^{3} + 6 x^{2} - 2 : 30

Maximum (4, 30)

Minimum (0, - 2), Maximum (4, 30)

What is the extreme f(x)=-x^3+6x^2-2 ?
The extreme f(x)=-x^3+6x^2-2 is Minimum(0,-2),Maximum(4,30)