MATH 1110 Midterm: MATH 1110 Cornell Exam Exam 2
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1. a) (5 points) let y(x) = x5 + 2. 5x + 2. Let f (x) = 2 sin(2x) + e x + x. Find f (n)(x), for n = 1, 2, 3, 4 and 5. (recall f (n) denotes the nth derivative of f . ) Consider the function f (x) = if x < 0 if 0 x < 1 if 1 x, where a and b are real numbers. sin(x) ax + b. 2. c) (8 points) for the values of a and b found in 2. a), write an expression for f (x) on the domain found in part 2. b) Problem 3. (9 points) let g(x) = 2x3 + 3x2 12x + 1. Find all points (x, g(x)) at which the tangent to g is horizontal. 4. a) (10 points) let f (x) = x, with domain [0, ). Use the de nition of the derivative to compute f (x).
