Homework from Section 4.5 4.5.3. - UCB Mathematics

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Homework from Section two positive numbers whose product is 100 and whose sum is a wantxandyso thatxy=100 andS=x+yis minimized. Sincexy=100,x6= we havey=100/x, so we want to minimizeS(x)=x+100/x. We find thatS (x)=1 100/x2. SettingS (x)=0 and solving forxyieldsx= 10. Since we arelooking for positive numbers, we takex=10. Notice that for 0<x<10,x2<100, so100/x2>1, which implies that 1 100/x2<0. ThusS (x)<0 for suchx. Similarly, forx>10,S (x)>0. It follows from the first derivative test thatx=0 is a minimum ofS(x). Thusx=10 andy=100/x=10 is a pair of positive numbers whose product is100 and whose sum is a minimum. the following problem: A farmer with 750 ft of fencing wants to enclosea rectangular area and then divide it into four pens with fencing parallel to one side ofthe rectangle. What is the largest possible total area of the four pens?(a) Draw several diagrams illustrating the situation, some with shallow, wide pens andsome with deep, narrow pens.

Homework from Section 4.5 4.5.3. Find two positive numbers whose product is 100 and whose sum is a minimum. We want x and y so that xy = 100 and S = x + y is minimized.

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