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3. (8 marks) Suppose that when a patient takes a blood thinner drug, the amount of drug (in mg) in the patient's blood can be modelled by: A(t) = te'ki where time t > 0 is measured in hours, and where k is some positive constant. (a) Find all critical point(s) of the Function A [where t > 0) and determine if they are local maximum(s) or minimum(s). Remember to find both t- and Avalues (i.e. both coordinates of the point). You should answer with exact values. and your answers might depend on k. (b) Fill in the blanks in the following sentences. (Note: If you are not printing the exam, you can write out the sentences and fill in the blanks.) For larger values of k the tvalue of the critical point would be [write "larger" or \"smaller\"), and for the patient, this means that for larger values of 1c, . [Write a sentence.) Furthermore, for larger values of k the Avalue of the critical point would be (write \"larger" or \"smaller\"). and for the patient. this means that for larger values of k, . (Write a sentence.)