AP Calculus ABmediummcq1 pt

Two positive numbers have sum 12. What is the maximum possible value of the product of the first number and the square of the second?

A.216216
B.256256
C.128128
D.432432

Explanation

Core Concept

Let the numbers be 12y12-y and yy, so P=(12y)y2=12y2y3P=(12-y)y^2=12y^2-y^3. P=3y(8y)=0P'=3y(8-y)=0 gives y=8y=8, and the maximum product is (4)(82)=256(4)(8^2)=256.

Correct Answer

B256256

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