What is the extreme f(x)=-2x^3+6x^2-7 ?

The extreme f(x)=-2x^3+6x^2-7 is Minimum(0,-7),Maximum(2,1)

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extreme f(x)=-2x^3+6x^2-7

extreme

Minimum (0, - 7), Maximum (2, 1)

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} - 7 : - 7

Minimum (0, - 7)

Plug

x = 2

into

- 2 x^{3} + 6 x^{2} - 7 : 1

Maximum (2, 1)

Minimum (0, - 7), Maximum (2, 1)

What is the extreme f(x)=-2x^3+6x^2-7 ?
The extreme f(x)=-2x^3+6x^2-7 is Minimum(0,-7),Maximum(2,1)