What is the extreme 2800x-x^3+3x^2+80x-500 ?

The extreme 2800x-x^3+3x^2+80x-500 is Minimum(-30,-57200),Maximum(32,61964)

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extreme 2800x-x^3+3x^2+80x-500

extreme

Minimum (- 30, - 57200), Maximum (32, 61964)

Solution steps

f^{'} (x) = - 3 x^{2} + 6 x + 2880

Find intervals:

Decreasing

: - \infty < x < - 30,

Increasing

: - 30 < x < 32,

Decreasing

: 32 < x < \infty

Plug

x = - 30

into

2800 x - x^{3} + 3 x^{2} + 80 x - 500 : - 57200

Minimum (- 30, - 57200)

Plug

x = 32

into

2800 x - x^{3} + 3 x^{2} + 80 x - 500 : 61964

Maximum (32, 61964)

Minimum (- 30, - 57200), Maximum (32, 61964)

What is the extreme 2800x-x^3+3x^2+80x-500 ?
The extreme 2800x-x^3+3x^2+80x-500 is Minimum(-30,-57200),Maximum(32,61964)