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

The extreme f(x)=-2x^3+6x^2-3 is Minimum(0,-3),Maximum(2,5)

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

extreme points

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

Minimum (0, - 3), Maximum (2, 5)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, - 3)

Plug

x = 2

into

- 2 x^{3} + 6 x^{2} - 3 : 5

Maximum (2, 5)

Minimum (0, - 3), Maximum (2, 5)

What is the extreme f(x)=-2x^3+6x^2-3 ?
The extreme f(x)=-2x^3+6x^2-3 is Minimum(0,-3),Maximum(2,5)