Answer Happy

7. (10 pts.) Sketch a curve y=f(x) based on the following information. You do not need to try to determine the function f. - The y-intercept is (−1,0). The three x-intercepts have x-coordinates −21+5​​,25​−1​, and 1 . - The derivative is f′(x)=2−3x2, and the domain of f is (−∞,∞). (a) Find the critical numbers of f, and determine the intervals on which f is increasing/decreasing. You do not need to find the exact values of f at any relative and/or absolute extrema, but for each critical number c, you must state whether f has a minimum, maximum, or neither at c. (b) Determine the intervals where the graph of f is concave up (CU) or concave down (CD). (c) Find the inflection point. (You do have enough information to find both coordinates of this point!) (d) On a separate sheet of graph paper, sketch a graph that agrees with all the information provided/asked for above. Please use either 2 or 4 graph squares per unit. (I.e., on each axis, the number 1 should be 2 or 4 grid lines away from the origin.)