3. Consider the function f(:i:) 2 (are """ where (t and I) are positive constants. 1i ((1.) Find the local uutxiuut, locul Ininiinn, and points of inflection. (b) How does varying e and b ull'ect the shape of the graph? (c) On the same set of axes, sketch the graph of the function for several values of a and b (three should be enough). (d) If we want the maximum of the function to occur at (2,3), what must the values of a and b be? NOTE: It often happens that we know from theoretical considerations that some physical (unease can be described by a function of a certain form with unknown parameters (like timeb\"E above). By performing experiments we can hope to nd enough data points to determine the parameters. Because there is always experimental error, it is easier (and more accurate) to t the parameters by looking for clearly dened features of the results (local maxes or mins, inection points) and adjusting the parameters so that these features occur at the points observed by experiment (i.e., some version of part ((1) above)