1. (20 pts) For what value of Then show that 2. (20 pts) x 2 k will f ( x) x k x 1 have a relative maximum at x 2 ? is a relative maximum. Determine whether Rolle's Theorem can be applied to f (x) on the closed interval [a, b]. x3 x 6 if x 1 and x is in [ 2, 3] f ( x) x 1 6 if x 1 3. (20 pts) Find the absolute maximum and minimum of the function 3 x x 3 f ( x) x2 x 4 3 4. (20 pts) f on [0, 2] , where for 0 x 1 for 1 x 2 Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. f ( x) 25 x 2 on [ 3, 4] A garden is to be laid out in a rectangular area and protected by a chicken wire fence. What is the largest possible area of the garden if only 100 running feet of chicken wire is available for the fence? 5. (20 pts) Bonus: (20 pts) Find a point on the graph of f ( x) x x 3 2 , where the tangent line is parallel to the line connecting between x 1 and x 2 (1, 5) and (2, 9)