Module 4 Discussion Worksheet - 3 3 f(t) -2 2 0 5 0 2 =1 =1 -2 Graph of f (t) Blank axes for sketching A(x) 1. Consider the function f(t) shown above. Let the function A(x) be defined by A(x) = ] f(t)dt. Answer the following, providing brief explanations based on the graph of f (t). a. On what interval(s) is A(x) increasing? Decreasing? b. For what value(s) of x does A(x) have a local maximum? Local minimum? c. On what interval(s) is A(x) concave up? Concave down? Linear? d. For what value(s) of x does A(x) have an inflection point?2. Determine the exact values of A(0), A(l), . . . , A(S) using the graph of f (t) and list them in the table below. -n---- ------- 3. Based on your responses to all the preceding questions, sketch the graph of A(x) on the blank axes provided on the rst page, doing your best to show linearity and concavity when needed. 4. Go to the following GeoGebra applet to answer the remaining questions: 11 s:ilwww. eo ebra.o classicim a Click on the point X from the origin and drag it to the right to see the graph of A(x) sketched before your very eyes. Does this graph conrm your answers for #1 3? Briey explain by lling out the table below. List the corresponding interval(s) in the second column and state the characteristic of f (t) in the third column (using words such as positive, negative, zero, constant, increasing, decreasing, concave up, concave dams, etc.) A(x) is 0n the interval Whileg) is Increasing Decreasing Linear Concave Up Concave Down