What is the extreme f(x)=-2x^3+36x^2-192x ?

The extreme f(x)=-2x^3+36x^2-192x is Minimum(4,-320),Maximum(8,-256)

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extreme f(x)=-2x^3+36x^2-192x

extreme

Minimum (4, - 320), Maximum (8, - 256)

Solution steps

f^{'} (x) = - 6 x^{2} + 72 x - 192

Find intervals:

Decreasing

: - \infty < x < 4,

Increasing

: 4 < x < 8,

Decreasing

: 8 < x < \infty

Plug

x = 4

into

- 2 x^{3} + 36 x^{2} - 192 x : - 320

Minimum (4, - 320)

Plug

x = 8

into

- 2 x^{3} + 36 x^{2} - 192 x : - 256

Maximum (8, - 256)

Minimum (4, - 320), Maximum (8, - 256)

What is the extreme f(x)=-2x^3+36x^2-192x ?
The extreme f(x)=-2x^3+36x^2-192x is Minimum(4,-320),Maximum(8,-256)