18. Suppose f(x) is the function whose graph is plotted below. 1 0.8 -0.5 0.6 0.4 0.2 Identify which one of the graphs plotted below is that of ƒ"(x). Indicate briefly on each of the other plots one reason why that one cannot be the graph of f"(x). (a) MAA 2.5 (b) NW V (c) 2.5 (d)

8. Graphs. Use the given graphs to answer the questions below. They are in no particular order Graph A Graph B Graph C a. Which graphs, if any, show a function with a derivative that is never negative? Circle all that apply. i. Graph A ii. Graph B iii. Graph C iv. None b. Which graphs, if any, show a function with a derivative that is always increasing? Circle all that apply. i. Graph A ii. Graph B iii. Graph C iv. None 9 (х), its c. The three graphs above, in no particular order, are of some function y derivative y = g'(x), and its second derivative y = g"(x). Label each graph appropriately. i. Graph A: ii. Graph B: iii. Graph C: ||

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)

Graph the following function f(x) = −2cos(4x + 180) + 3 by hand on a grid paper. Be sure to state the amplitude, period, phase shift, and equation of midline/axis of curve. Be sure to clearly show your scale on the x and y axes.