9. a. If the graph of the function g(x) = (x - 1)(x - 4) ax + b has a horizontal tangent at point (2, -1), determine the values of a and b. b. Sketch the function g. 10. Sketch each function using suitable techniques. a. y = x4 - 8x2 + 7 d. y = x(x - 4)3 b. f(x ) = 3x - 1 X x +1 e. h(x) = 2 _ 4x+ 4 X x + 1 12 - 3+ + 2 c. g(x) = 4x2 - 9 f. f (t ) = 1 - 3 1 1. a. Determine the conditions on parameter & such that the function f(x) = 2 _ 2 will have critical points. b. Select a value for k that satisfies the constraint established in part a, and sketch the section of the curve that lies in the domain (x s k. 12. Determine the equation of the oblique asymptote in the form y = mx + b for each function, and then show that lim [y - f(x) ] = 0. * +00 a. f(x) = 2x - 7x + 5 b. f (x ) = 4x3 - x2 - 15x - 50 2x - 1 x2 - 3x 13. Determine the critical numbers and the intervals on which g(x) = (x2 - 4)2 is increasing or decreasing. 14. Use the second derivative test to identify all maximum and minimum values of f(x) = x3 + 5x2 - 7x + 5 on the interval -4 x