For the function f(x)=x2 compute each average rate of change: (a) From 1 to 2 (b) From 1 to 1.5 (c) From 1 to 1.1 (d) From 1 to 1.01 (e) From 1 to 1.001 (f) Use a graphing utility to graph each of the secant lines along with . (g) What do you think is happening to the secant lines? (h) What is happening to the slopes of the secant lines? Is there some number that they are getting closer to? What is that number?

The chart below shows the average depth of water in a river for 3 different months of the year. What is the best approximation for the depth of the river for the month of June (the 6th month of the year)? AVERAGE DEPTH MONTH (in feet) January 11 May 28 September 12 HINT: If you cannot find the instantaneous rate of change (tangent slope) the next best thing is the average rate of change (secant slope)! 13 feet 17 feet 79 feet 4 20 feet 24 feet

The area of a circle as a function of radius is A(r) =Πr² , with area measured in cm² and radius measured in centimeters. Find the derivative of area with respect to radius. On a geometric diagram, illustrate the area corresponding to Δ A = A(r + Δr) − A(r). What is a geometric interpretation of the derivative? Do the units make sense?

The graph of a function is given. y (a) Determine the net change between the Indicated points on the graph. (b) Determine the average rate of change between the incicated points on the graph.

At 1 p.m., snail A is 9 ft west of snail B. Snail A moves north at 2 ft/hr and snail B moves south at 2 ft/hr. How fast is the distance between the snails changing at 4 p.m.? (a) Draw a diagram for this scenario. Create and label each variable. (b) What is known/given? What needs to be found? (c) Use your diagram to determine a function relating the variables in this scenario. (d) Find the appropriate rate