MAT-1110 Midterm: MATH 1110 App State summer2017 Test2
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Show your work: (11 points) implicit di erentiation. (a) use implicit di erentiation to nd at (x, y) = (1, 2). dy dx given y2 xy+x3 = 3. P4(x) = 1 2(x 3) + 4(x 3)3 . Either ll in the blank or circle not enough info. if there isn"t enough information to nd the answer. The linearization of g(x) based at x = 3 is. Or not enough info: (10 points) use newton"s method to approximate a solution of x3 + 1 = x2. Use the initial guess x0 = 1 and work through 2 iterations. Write g (x) in terms of f (x) and f (x) and then use that to compute g (1). (c) suppose that h(x) = f 1(x). Write h (x) in terms of f (x), f 1(x), and f (x) and then use that to compute h (2): (15 points) derive the formula for the derivative. (a) find d dx.
