MTH254-RecAct-Week6.pdf

B at the bugs position after t 8 seconds how fast is

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(b) At the bug’s position after t = 8 seconds how fast is the temperature that the bug feels changing per second? (i.e. What is ∂T/∂t for the bug?) (c) At the bug’s position after t = 8 seconds how fast is the temperature that the bug feels changing per centimeter? (i.e. What is the change in temperature in the direction the bug is moving at t = 8? You may want to think in terms of directional derivatives.) (2) Find the directions in which the directional derivative of f ( x, y ) = x 2 +sin( xy ) at the point (1 , 0) has the value 1. Definition : The critical points of a function z = f ( x, y ) are the points ( a, b ) such that f x ( a, b ) = 0 and f y ( a, b ) = 0, (i.e. f ( a, b ) = ~ 0). (3) Find all of the critical points of f ( x, y ) = x 3 - 2 y 2 - 2 y 4 + 3 x 2 y .

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Math 254 Week 6 Recitation Activity - Fall 2018 Page 2 of 2 (4) The quantity, Q , of apples purchased at a store, in kilograms per week, is a function of the price of apples, a , and the price of pears, p , both in dollars per kilogram. (a) Do you expect ∂Q/∂a to be positive or negative? Explain (b) Do you expect ∂Q/∂p to be positive or negative? Explain (c) Interpret the statement “when the price of apples is \$3 per kilogram and the price of pears is \$4 per kilogram
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• Fall '09
• Hellin
• Absolute Zero, Celsius, assistant manager, Centimetre gram second system of units, Thermodynamic temperature

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