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Unformatted text preview: 3 , where x = t 2 and y = 1-2 t . Find dz/dt in the following two ways. A. Express z explicitly as a function of t and dierentiate. B. Use the Chain Rule for partial derivatives, expressing your answer as a function of t . 1 Problem 6 . 40 pts. Consider the function f ( x, y ) = x + xy 2 . A. Find the directional derivative of f at the point P (1 , 2) in the direction of the vector-3 i + 4 j . B. In what direction should you go from P to get the greatest rate of change in f ? What is this maximum rate of change? 2 EXAM Exam 1 Math 2350-02, Spring 2008 Feb. 20, 2008 Write all of your answers on separate sheets of paper. You can keep the exam questions when you leave. You may leave when nished. You must show enough work to justify your answers. Unless otherwise instructed, give exact answers, not approximations (e.g., 2, not 1 . 414). This exam has 6 problems. There are 240 points total . Good luck!...
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