MA 2113 Midterm: MATH 221 MSState math 221 Practice Exam 1 ans key
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7: 1, (x) = 4x + 1, f (x) = (3x2 + 3)(x2 + 7) (x3 + 3x 1)(2x) (x2 + 7)2, y = 2000(3x3 + 2)1999. (9x2: h (r) = 25(5r 6)4(r3. 7y6 + 2x3y 2y: y = 65x + 1, y = x + 6 h (x) = 4x2(x 3) and h (x) = 12x(x 2). The critical values are x = 0 and x = 3. The critical points are (0, 0) and (3, 27). The function is increasing on (3, ) and decreasing on ( , 0) (0, 3). The function is concave up on ( , 0) (2, ) and concave down on (0, 2). There is a local minimum at (3, 27) which is also an absolute minimum, and the in ection points occur at x = 0 and x = 2: the two numbers are 50 and 50.
