The reaction R(x) of a patient to a drug dose size of x depends on the type of drug. For a certain drug, it was determined that a good description of the relationship is :R(x)= Ax^2(B-x) on domain [0,B]

Question

The reaction R(x) of a patient to a drug dose size of x depends on the type of drug. For a certain drug, it was determined that a good description of the relationship is :R(x)= Ax^2(B-x)     on domain [0,B]
where A and B are positive constants . The sensitivity of the patient's body to the drug is defined to be R'(X)
a) for what value of x is the reaction a max and what is the max reaction value
b) for what value of x is the sensitivity a maximum? what is that maximum sensitivity?

oobleck · Answer

R' = 2Ax(B-x) - Ax^2 = Ax(2B-3x) (a) R'=0 when x=0,2B/3 R" = A(2B-3x) - 3Ax = 2A(B-3x) (b) R"=0 when x=B/3