Name:________________________ Date:________________________ AP Calculus BC Class Activity 4b: Optimization 1. Find two numbers such that the sum of the first and three times the second is 24 and their product is a maximum. 2. Find the point on the curve that is closest to the point (4, 0)? Hint: You will need to use the distance formula: . 3. A rectangular page is to contain 25 square inches of print. The margins on each side are 2 inches. Find the dimensions of the page such that the least amount of paper is used. 4. Find the dimensions of the rectangle that is bounded by the x-axis and the top half of the ellipse and has the maximum area. Hint: Area (rectangle) = 2xy.

# bccalcclassact4boptimize

Name:________________________ Date:________________________ AP Calculus BC Class Activity 4b: Optimization 1. Find two numbers such that the sum of the first and three times the second is 24 and their product is a maximum. 2. Find the point on the curve that is closest to the point (4, 0)? Hint: You will need to use the distance formula: . 3. A rectangular page is to contain 25 square inches of print. The margins on each side are 2 inches. Find the dimensions of the page such that the least amount of paper is used. 4. Find the dimensions of the rectangle that is bounded by the x-axis and the top half of the ellipse and has the maximum area. Hint: Area (rectangle) = 2xy.

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