What is the extreme f(x)=-2x^3+9x^2-12x ?

The extreme f(x)=-2x^3+9x^2-12x is Minimum(1,-5),Maximum(2,-4)

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extreme f(x)=-2x^3+9x^2-12x

extreme

Minimum (1, - 5), Maximum (2, - 4)

Solution steps

f^{'} (x) = - 6 x^{2} + 18 x - 12

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 1

into

- 2 x^{3} + 9 x^{2} - 12 x : - 5

Minimum (1, - 5)

Plug

x = 2

into

- 2 x^{3} + 9 x^{2} - 12 x : - 4

Maximum (2, - 4)

Minimum (1, - 5), Maximum (2, - 4)

What is the extreme f(x)=-2x^3+9x^2-12x ?
The extreme f(x)=-2x^3+9x^2-12x is Minimum(1,-5),Maximum(2,-4)