8. A function is called even if f(x) = f(-x) and a function is odd if f(r) = f(-x). Suppose that f is differentiable. (i) If f is odd, show that f' is even. (ii) If f is even, show that f' islodd. 9. The gas law for an ideal gas at absolute temperature I (in kelvin), pressure P (in atmospheres), and volume V (in liters) is PV - nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Assume n is constant. In this scenario, suppose that pressure P(t) and volume V(t) are changing with respect to time and are differentiable functions