Math 127 Lab Worksheet 6 Sections 14 3 and 14 4 Short Descriptions and Formulas Group Work Portion of the Worksheet Names Work in groups to do this portion of the worksheet Make sure to take parts in solving the problems Your lab attendance is not simply a matter of being present but of being prepared willing to explore the problem working in groups and contributing toward the solution 1 Background Story Partial derivatives keep showing up in many areas Here is a business appli cation example Questions At a distance of x feet from the beach the price of a plot of land of area a square feet is f a x i What are the units of fa a x a What does fa 1000 470 7 mean in practical terms b What are the units of fx a x c What does fx 1000 470 4 mean in practical terms d Which is cheaper i 1005 square feet that are 475 feet from the beach ii 995 square feet that are 468 feet from the beach Justify your answer 2 2 Background Story A common error evaluating any derivative at a point is forgetting to plug in the numbers Questions A student was asked to find the equation of the tangent plane to the surface z x3 y2 at the point x y 5 2 The student answered z 2y x 5 3x2 y 2 121 A At a glance how do you know this is wrong B What mistakes did the student make C Answer the question correctly 3 3 Background Story Sometimes the linearization is a hyperplane in R4 Questions Approximate cid 112 3 14 2 1 93 2 6 07 2 using a linear approximation 1 1Video https youtu be ck5GnrW1HkI 4 4 Find an equation of the tangent line to the graph of f x y xey at 5 0 in the y direction 5 Compute the first order partial derivatives of w x y z 5y 3x 33z Individual Portion of the Worksheet Name Upload this section individually on Canvas You can ask questions in class and work in groups but you turn in the individual work Start before the class so you can ask questions during the class If you didn t complete the work in class make sure to work on it outside the class and complete it Show all your work your score depends on the work you have shown Individual Portion s of Worksheet Rubric Completion 1 Accuracy 7 Completion grade is assigned 0 if worksheet not begun or if there is no work for answers 0 5 if started but incomplete 1 if clear effort to complete all problems is shown Accuracy grade is assigned for the problems that are graded All questions for individual work for this week are posted in Worksheet 5 This worksheet contains no individual question 5