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) = tekt 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 maximums/minimums. Remember to find both t- and A-values. Answer with exact values.

(b) Fill in the blanks in the following sentences.

1. 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).

2. 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).