MAT-1110 Midterm: MATH 1110 App State summer2017 Test2 answer key
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Show your work! (a) use implicit di erentiation to nd at (x, y) = (1, 2). dy dx given y2 xy+x3 = 3. Then nd the equation of the line tangent to y2 xy+x3 = 3. To di erentiate y2 we need the chain rule 2yy (think of y as the inside func- tion). To di erentiate xy we need the product rule. We get 2yy 1y xy + Next, we need to evaluate the derivative at our point: 2(2) 1 and so y 2 = 1. Now we have a point (x, y) = (1, 2) and a slope m = 1/3 y (cid:12)(cid:12)(cid:12)(x,y)=(1,2) 3 (x 1) and so y = y 3x2. 3 x y = f (x) (b) use implicit di erentiation to nd dy dx given x2 + 5x + ey = y2 + 1. Again, we need the chain rule to di erentiating both ey and y2.
