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'\" where time t > O 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 A-values (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 k, . (Write a sentence.) Furthermore, for larger values of is: the Avalue of the critical point would be (write l'larger" or "smaller"), and for the patient, this means that for larger values of k, . (Write a sentence.)