HillE's function models how the amount of oxygen bound to hemoglobin in the blood depends on oxygen concentration, P, in the surrounding tissues. In its most general form Hillj's function models the fraction of hemoglobin molecules in blood that are bound to oxygen by using the following formula, where k is a positive constant, and n is a positive integer. Pn k\"+P" KP) = (a) Calculate f'(P). (b) Show that f'(P) > 0 for all P > 0. This result means that increasing the oxygen concentration always increases the fraction of hemoglobin molecules that are bound to oxygen. Differentiate the function with respect to the independent variable. 2 f(x ) = - (1 -3X 2 15Druzinsky (1993) showed that chewing frequency (i.e., the number of times an animal chews in one minute) is proportional to its body mass raised to the power of -0.128, that is, if M is the body mass and c the chewing frequency, then C= KM-0.128 for some positive constant k. (a) Assume that the body mass of a particular mammal is given by a formula M(t) = 1 + 2vt. Calculate - (b) Druzinsky also found that the jaw length of the animal, L, is proportional to its body mass raised to the 0.312 power, i.e., L = M. where r is another positive constant. Calculate dc , the rate of chewing frequency with jaw length.Find the lines that are (a) tangential and (b) normal to each curve at the given point