Flu Algebra problem (someone help please )

Question

A flu patient is prescribed a course of an antivirus drug. The number of mg of the drug in the bloodstream 𝑡 hours after the first dose is taken is given by the function 𝐴(𝑡) = 400𝑡𝑒^-3t

a. Sketch the graph of the function in an appropriate window, labeling axes and scale.

b.On what interval(s) is the amount of drug in the bloodstream increasing? Decreasing?

c.When is the amount of the drug at a maximum? Label the corresponding point on the graph.

Answer 1

a. Choose some value of t, such as t = 0, 1/3, 1, ... to sketch the graph.

b. Find A'(t), let A'(t) = 0, you will find a critical point at t = 1/3. So, the function increases when < t < 1/3 and decreases when t >1/3.

c. This is already solved in b. The function reaches its maximum at t = 1/3.