Question

How do you find on what time interval is the concentration of the drug increasing if suppose a certain drug is administered to a patient, with the percent of concentration in the bloodstream t hr later given by K(t)=8tt2+1?

Answer 1

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Answer 2

Answer:

Hopefully this helps!

Step-by-step explanation:

You will need to start by differentiating.

K'(t)=8(t2+1)−8t(2t)(t2+1)2

K'(t)=8t2+8−16t2(t2+1)2

K'(t)=8−8t2t2+1

This will have a critical number when K'(t)=0.

0=8−8t2

8t2=8

t=±1

But since t>0, only t=1 is acceptable.

You will notice that whenever t>1, the derivative turns negative, therefore the amount of drug in the patients system is increasing for the first hour, with 0≤t<1.

Hopefully this helps!