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Unformatted text preview: 3 , where x = t 2 and y = 12 t . Find dz/dt in the following two ways. A. Express z explicitly as a function of t and diﬀerentiate. 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 vector3 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 235002, 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 ﬁnished. • 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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 Spring '09
 CAKMAK
 Calculus, Derivative, Angles, pts

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