In 1956 American geologist and geophysicist M. King Hubbert attempted to predict the total amount of oil reserves in the United States. King did this by assuming that the total amount of oil produced would follow a logistic curve, implying that the rate of production would be governed by the derivative of the logistic curve (often called the Hubbert curve in this area). Assume that the Hubbert hypothesis is correct -- the total amount of oil production is given by a logistic curve. At what value of P is the rate of production P'(t) the largest