Answered: For the following functions, (1) find…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The demand for ACME Q-bits is given by the function q = f(Y,p), where • q = monthly demand for ACME Q-bits (measured in 1000s of Q-bits) • Y= average monthly income in the Q-bit market (measured in $1000s) •p = price/Q-bit that ACME sets (measured in dollars). When average monthly income is $4500 and ACME's price is $35... • q = 22, aq/əY = 0.77 aq/ap = - 0.64 If average monthly income increases to $4700, by approximately how much can ACME increase their price while keeping demand for the product fixed at q = 22? Hint: Use linear approximation.
2. Determine the critical points of the function: R(y) = y² – 6y Enter vour answer
Find the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum, or a saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the critical points. f(x,y) = 5 + 2x? + 6y? What are the critical points? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The critical point(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no critical points.

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For the following functions, (1) find the critical values and (2) determine if at these points the function is at a relative maximum, relative minimum, inflection point, or saddle point. (I) f (x, y) = 60 + (x-y)3 + (y-1)3 (II) f (x, y) = 2 + x2 + y2