A Background: A somewhat obscure mathematical function is the inverse hyperbolic cosecant. It is used seldom enough that it does not have its own key on a standard scientific calculator, but it has a rather complicated definition that involves taking squaring, and taking reciprocals, square roots and a logarithm. In this assignment, we'll just call it / Back before everyone had ready access to powerful computers, in order to determine the values of this function, one might have looked up values for this function in a handbook of mathematical tables. A piece of one of those tables is provided in the following table. X 10 12 1.4 1.6. 1.8. 20 f(x) 0.88 0.76 0.66 0.59 0.53 0.48 1. Plot the points and decide, based on your plot, whether the function is a. Increasing, constant or decreasing, and b. Concave up or concave down • You may need to plot these points very carefully in order to see exactly which way the curve bends. (Hints: It really does bend either up or down; it does not change concavity.) • You will want to upload a scan of your plot as part of your post. If you are happy with your plot, you do not need to post it a second time when you make your final post. 2. a. Calculate the average rate of change in / between x 1.0 and x 1.2. b. Calculate the average rate of change in / between x 1.8 and x=2.0. c. Does the average rate of change increase, decrease, or remain constant as you move from inputs that are a little larger than 1.0 to inputs that are a little smaller than 2.0? 3. Explain whether your answers to parts 1b and 2care consistent. . You may find it helpful to recall that when a function is concave up, its average rate of change is increasing (which includes becoming less negative if the AROC is negative), but when a function is concave down, its average rate of change in decreasing (which includes becoming more negative if the AROC is negative) 4. a. Use interpolation to estimate (1.07), and round your answer to two decimal places a. Use the concavity of/ to determine whether your interpolation estimate is an overestimate .e. larger than the "true" value of A1.07)) or an underestimate lie, smaller than the "true" value of 11.07.