(a). Consider the parabolic function f(x) =ax +bx+c, where a #0, b and care constants. For what values of a, band c is f concave up? 11) concave down?(b). A mathematical biologist is created a model to administer medicine reaction (measured in change of blood pressure or temperature) with the model given by R = m- m N 3 where c is a positive constant and m is the amount of medicine absorbed into the blood. The sensitivity to the medication is defined to be the rate of change of reaction R with respect to the amount of medicine m absorbed in the blood.Find the sensitivity, R'. (i) Find the amount of medicine that is being absorbed into the blood when the reaction is maximum. (mi) Find the instantaneous rate of change of sensitivity with respect to the amount of medicine absorbed in the blood. (iv) Find the amount of medicine that is being absorbed into the blood when the sensitivity is maximum.(c). It is well known that the rate of flow can be found by measuring the volume of blood that flows past a point in a given time period. The volume /' of blood flow through the blood vessel is V = 2avr dr where v= K ( R' -r? ) is the velocity of the blood through a vessel. In the velocity of the blood through a vessel, K is a constant, the maximum velocity of the blood, R is a constant, the radius of the blood vessel and r is the distance of the particular corpuscle from the center of the blood vessel. () If R=0.30 cm and v= (0.30-3.33r?) cm/s, find the volume. (ii) Construct and develop a general formula for the volume I' of the blood flow.(d). Find the area of the region enclosed by the graphs of f (x) = x and g(x)=x- +2x.{c}. Find the 31123 ofthe region EClSt'd by the graphs of y = E and y = 41