1. If the slope of the graph of g(t) at (-3,6) is -1.5, find the equation of the tangent line (in modified point slope form) at this point and then use it to approximate g(2). 2. The graph of g(t) is shown. Trace this graph accurately on your paper and use it to sketch a graph of g'(t) g(t) 3. Given the graph f (t), determine at what value(s) of "t" are a - c true? ( (t) (use integers -5 thru 5 from the graph). a) f'(t) is the least b) interval(s) where fis negative c) f '(t) = 0 d) interval(s) where f' is decreasing 4. Let C(t) be the number of students majoring in chemistry where t is the number of years since 2010. 600 500 You do not need to sketch this figure on your 400 paper but you do need to show your work. 300 # of students 200 100 1 2 3 4 5 6 7 8 9 years a) Find the average rate of change in O(t) over the interval 3 S t $ 8. Explain the meaning of your answer. b) Estimate C'(2). Explain the meaning of your answer. Remember units. c) in what year(s) is C' (t) = 0. Explain briefly where these values are found graphically. 5. For some painkillers, the size of the dose, D, given depends on the weight of the patient, W. Thus, D = f (W), where D is in milligrams and Wis in pounds. Interpretations must include full sentences complete with units. (a) Interpret the statement f' (150) = 0.25 in terms of this problem. Include units. (b) Using the info given in a) and if f (150) = 9, estimate f (155). Explain or show supporting work. (c) Interpret the statement f-1(12) = 160 in terms of this problem. Include units. (d) What are the units of (f-1)