75%(4)3 out of 4 people found this document helpful
This preview shows page 1 - 3 out of 8 pages.
4/9/21, 9:15 AMSouthern New Hampshire University - 6-3 Module Six Problem SetPage 1 of 8[PRINT]MAT-225-X4741 21EW4 Calc I: Single-Variable Calc, 6-3 Module Six Problem Set Dallas Weber, 4/6/21 at 9:12:08 AM EDTQuestion1:Score 3/6Find two numbers with difference and whose product is a minimum.Enter your answers in increasing order.First number:Your responseCorrect response-68-68Auto gradedGrade:2/2.0 Second Number:Your responseCorrect response6868Auto gradedGrade:1/1.0 Show your work and explain, in your own words, how you arrived at your answers.x-y=136y=x-136The product of the two numbers is a minimum:xy=x(x-136)f(x)=x^2-136xSet the derivative to 0 for critcal points:f'(x)=2x-136=02x=136-68,68 UngradedGrade:0/3.0Total grade: 1.0×2/6 + 1.0×1/6 + 0.0×3/6 = 33% + 17% + 0%Feedback:The following is Mobius' explanation for a solution to this question. You can use this and other onlinereferences as a guide, but your explanation should be in your own words.Let be the smaller number and be the larger number. The product of the two numbers is.If the difference between and is , then . Substitute this formula for into the formula for to get.Differentiate with respect to to obtain.Solve to find the critical numbers.Thus, the critical number is .136!!"xyP=xyxy136y=x+ 136yPP=x(x+ 136) =+ 136xx2x= 2x+ 136dPdx= 0dPdx2x+ 136 = 02x=-136x=-68x=-682
4/9/21, 9:15 AMSouthern New Hampshire University - 6-3 Module Six Problem SetPage 2 of 8Since , by the Second Derivative Test, is a local minimum. Therefore, the twonumbers are and .Question2:Score 3/3A farmer wants to fence a rectangular area of square feet next to a river. Find the length and width of the rectangle which uses the leastamount of fencing if no fencing is needed along the river. Assume the length of the fence runs parallel to the river.Length: Your responseCorrect response1212Auto gradedGrade:1/1.0 feetWidth: Your responseCorrect response66Auto gradedGrade:1/1.0 feetTotal grade: 1.0×1/2 + 1.0×1/2 = 50% + 50%Feedback:Let be the width and be the length. The amount of fencing required is.If the area required is , then or . Substitute this formula for into the formula for to get.Differentiate with respect to to obtain.Solve to find the critical numbers.Thus, the critical numbers are . Since the width must be greater than zero, we need only consider .