lultiple Choice dentify the choice that best completes the statement or answers
ID: 2885688 • Letter: L
Question
lultiple Choice dentify the choice that best completes the statement or answers the question. Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum. 1. a. 28 and 28 b. 28 and 14 c. 22 and 17 d. 34 and 11 e. 24 and 16 2. Complete two iterations of Newton's Method for the function fx)-2 -7 using the initial guess 2.6. Round your answers to four decimal places. a. 2.6463,2.6456 b. 2.6463,2.6460 c. 2.6463,2.6459 d. 2.6459,2.6457 e. 2.6462, 2.6458Explanation / Answer
1. Sum of first and twice the second is 56
let the numbers be a and b
a+2b = 56
a = 56-2b
product (P) = a*b = (56-2b)*b = 56b - 2b^2
P is maximum where first derivative is 0
dP/db =56 - 4b = 0
b = 14
a = 56-2*14 = 28
so answer is option b
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