5 drivegooglecom C o HWFocu52.pdf - Geog... r N FOCUS PROBLEMS: Your goal for the focus problem should be to clearly demonstrate your understanding of the concepts and/or skills we have been studying in class. Assessment of your work will be based on completeness, correctness, and presentation. Please refer to the Focus Problem Guidelines for details on the presentation of your work. This is your weekly report and should reect your most professional presentation. All problems are to be done with methods taught in this course. The focus problem solutions are worth 12 points. 1) (3 pts) Consider the function f (x) = 3x1 5x + 2. a) Use the limit denition of the derivative to nd a formula for f '(x). Clearly show your algebraic process. b) Use Desmos to graph both f (x) and f'(x) on the same axes. Choose two distinct features of the graph of f '(x) and explain how they relate to the graph of f (1:) Include the Desmos graph in your submission. (3 pts) The value, V, of a particular automobile (in dollars) depends on the number of miles, m, the car has been driven, according to the inction V = h(m). a) Suppose that h(50000) = 15000 and h(65000) = 12800. What is the average rate of change of h on the interval [50000, 65000], and what are the units on this value? b) In addition to the information given in (a), say that h(80000) = 10900. Determine the best possible estimate of h'(65000) and write one sentence to explain the meaning of your result, including units on your