1. According to Kleiber's law the metabolic rate q of the vast majority of animals is related to the animal's mass M according to
q = kM3/4
where k is a constant. This means that a cat, with mass about 100 times that of a mouse, has a metabolism about 1003/4 ≈ 32 times greater than that of a mouse. Find the function that describes the rate of change of the metabolic rate with respect to mass.
2. The monthly output of a certain product is
Q(x) = 800x5/2
where x is the capital investment in millions of dollars. Find dQ/dx, which can be used to estimate the effect on the output if an additional capital investment of $1 million is made.