Final answer:
To find the number b such that the average rate of change of f on the interval (2, b) is -(1/10), we need to solve a quadratic equation derived from the average rate of change formula.
Step-by-step explanation:
To find the number b such that the average rate of change of f on the interval (2, b) is -(1/10), we need to calculate the average rate of change of f and then set it equal to -(1/10). The average rate of change of a function on an interval is given by the formula: average rate of change = (f(b) - f(a))/(b - a). In this case, we have f(x) = 1/x and the interval is (2, b). So, we need to set up the equation: (1/b) - (1/2))/(b - 2) = -(1/10).
To solve this equation, we can multiply both sides by 10(b - 2) to eliminate the denominators. This will give us a quadratic equation that we can solve for b.