MATH 0220 Midterm: Math 0220 Math0220-05-2-231
Document Summary
Given f (x) = x2 + 1, use the de nition of the derivative to show that f (x) = 2x. Find the equation of the line tangent to the curve of y = x1/3 at x = 1000. (note: (1000)1/3 = 10. ) Use the tangent line in part (b) to obtain an approximation for (1005)1/3. Approximate 2 by applying newton"s method to approximate the positive zero of the function f (x) = x2 2 with x1 = 1. 5. Find x2. (you do have to show your work. ) Let y = ln x x3 + 1. Let y = (1 + 2x x3)100. Given y 3 + xy + e2x = 2, nd dy dx at (0, 1). 2: let f (x) = 2x3 3x2 12x + 5, < x 4. Then f (x) = 6x2 6x 12 = Find the intervals on which f (x) is increasing or decreasing. Find the local maxima and local minima of f (x).
