antidifferentiation: find maximum value, profile, etc

[Guest]

2) The concentration of a certain drug in the bloodstream is given by the rule C(t) = 3te^(−1.1t), where t is the number of hours since the drug was taken.

b) The drug is effective only if its concentration is at least 57% of its maximum value.
i) Use calculus to find the maximum value.
ii) Between what times is it effective? Give answers to nearest hundredth of an hour.

c) The ‘profile’ of the drug is a definite integral of the concentration, with terminals equal to the limits of the time during which it is effective. Write this definite integral.

d) Evaluate this definite integral.

 

[skeeter]

this is a straight forward problem ...

find dC/dt, set dC/dt = 0 and find the value of t when the concentration is a max.

let T = time found above when C(t) is a maximum.

set C(t) = (.57)*C(T) and solve for t ... you will get two solutions for t which will be the upper and lower limits of integration for the integral problem.