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September 20, 2014

Homework Help: calculus

Posted by casidhe on Friday, April 20, 2012 at 11:41pm.

I've posted this question before and think I've made some progress but it some part of the second answer I got is wrong

I've done the first question but I cannot get any farther. I'm so stuck. Please explain or just help me to figure out the next steps.

A printed poster is to have a total area of 837 square inches with top and bottom margins of 7 inches and side margins of 6 inches. What should be the dimensions of the poster so that the printed area be as large as possible?

*To solve this problem let x denote the width of the poster and let y denote the length. We need to maximize the following function of x and y:
ANSWER:(x-12)(y-14)

*We can reexpress this as the following function of x alone:ANSWER: f(x)=(x-12)(837/x-12)+14


*We find that f(x) has a critical number at x=_________

*To verify that f(x) has a maximum at this critical number we compute the second derivative f(x) and find that its value at the critical number is_________, a negative number.

*Thus the optimal dimensions of the poster are ________ inches in width and ________ inches in height giving us a maximal printed area of ________square inches.

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