Math 20C Spring 1995Exam 2HeltonGive explanations which tell us clearly every step of what you are doing.LetF(x, y, z)=(x2+y2x2)+x+ 100. Suppose the graph ofFrepresents a shiny smoothhill.1.What are the partial derivatives ofFwith respect toxandy.2.What is the gradient?Suppose you are standing over the pointx=1,y= 2 on the hill.3.If you drop a marble, in which direction will it start to roll? You only need to specifythe direction in thex, yplane which it will take.4.What is the slope of the hill in the direction of the vector (2,4)?5.Suppose you lay a ruler (1 foot) down on the hill pointing in the northeast directionwith one tip at your feet. Approximately how much higher is the other tip? Here we
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