MATH 101 Exam 2, Fall 2002

VRBERICAN TON SIT LIBEL ARY OF BEIRCI : Time: | hour “MATH 101 Quiz II First Semester 02-03 1.Find the first derivative for the following functions: a Reet Lt u we vu 8 b. Y= (2x+1)*(x74+3x) c Y= xt+l d. S=sin'(10 - 3t’) 2. a. Find equations for the tangent and normal to the curve y = cotx at the point (2, 0). 2 b. Sketch the curve y = cotx for (0,7). Also sketch the tangent and normal whose equations were found in (a) . l os t 3.Find “att =0 ify =cos2x and x= £47. dt 2 4 ere aoe Ly d*y 4.Using implicit differentiation, find “and j for xy +2x+3y =20. dx dx 5.Given the function f(x) = -x*+6x?-9x+3, defined on (- 2,5] a. Find the intervals on which the function is increasing and those on which it is decreasing. Identify (find the coordinates) any local maxima or minima of the function. b. Find intervals on which the function is concave up and those on which it is concave down. Does f(x) have a point of inflection? If so, identify it. c. Sketch the curve of f(x). d. Find the absolute extreme values of the function, if they exist. Discuss.