How do I answer each part of this question?

Question

The quantity of a drug in the blood stream t minutes after the tablet is swallowed is given, in mg, by

𝑄(𝑡) = 50𝑡𝑒^−.01𝑡

a.) At what time is the quantity of the drug in the bloodstream a maximum?

b.) What is that maximum?

Answer 1

Ayana,

You can use properties of the first derivative to find when the function is a maximum. Just find the critical points where Q'(t) is equal to 0 or undefined, and then determine if the point is a maximum by checking to see if Q'(t) changes from positive to negative at the point.

For part b, just plug in the time you found in part a into the equation for Q.