Problem 3. A hole is made in the bottom of a water bottle. Let h(t) be the height of the water level in the bottle in centimetres (cm) at t seconds (s) after the hole is made. Suppose that h(t) = (5 - )2. In this question you can use the fact that the derivative of f(x) = ax2 + ba + c is f'(x) = 2ax + b. 1. What is the average rate of change of the height of the water level between the time when the hole is made and the time when the bottle becomes empty? 2. When is the height of the water level decreasing the fastest? 3. Estimate h(10.1) without calculating it directly