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To find critical numbers or critical points, find out where the derivative equals 0.

The function is 4x3-60x2+288x-432.

It's derivative then is 12x2-120x+288, set that equal to 0 to find critical points: 12x2-120x+288 = 0

Factor out a 12:

12(x2-10+24) = 0

Divide both sides by 12:

x2-10+24 = 0

Factor:

(x-6)(x-4) = 0

(x-6) = 0 or (x-4) = 0

x = 6 or x = 4The critical numbers are 6 and 4.

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Q: What are the critical numbers of 4 x to the third power minus 60 x squared plus 288 x minus 432?
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