Explain why the function is differentiable at the given point. f(x, y) = 4 + x ln(xy − 9), (5, 2) The partial derivatives are fx(x, y) = Correct: Your answer is correct. and fy(x, y) = Correct: Your answer is correct. , so fx(5, 2) = 10 Correct: Your answer is correct. and fy(5, 2) = 25 Correct: Your answer is correct. . Both fx and fy are continuous functions for xy > Incorrect: Your answer is incorrect. and f is differentiable at (5, 2). Find the linearization L(x, y) of f(x, y) at (5, 2). L(x, y) =

Suppose there is a simple index of three stocks, stock abc, stock xyz, and stock qrs. stock abc opens on day 1 with 4000 shares at $3.15 per share. stock xyz opens on day 1 with 5000 shares at $4.30 per share. stock qrs opens on day 1 with 6000 shares at $4.60 per share. the price of stock abc on day 8 begins at $3.50. the price of stock xyz on day 8 begins at $3.90. stock qrs opens on day 8 with a price of $4.50 per share. assume that each stock has the same number of shares that it opened with on day 1. what is the rate of change of this simple index over 1 week?

Abike shop sells you a bicycle for $63 and a helmet for $21. the total cost is 150% of what the shop spent originally. how much did the shop spend originally? how much profit did the bike shop earn by selling the bicycle and helmet to you ?

Marco is studying a type of mold that grows at a fast rate. he created the function f(x) = 345(1.30)x to model the number of mold spores per week. what does the 1.30 represent? how many mold spores are there after 4 weeks? round your answer to the nearest whole number. 1.30 represents the number of mold spores marco had at the beginning of the study; 985 mold spores 1.30 represents the number of mold spores grown in a given week; 448 mold spores 1.30 represents the 30% rate of weekly growth; 345 mold spores 1.30 represents the 30% rate of weekly growth; 985 mold spores