MATH 1306 – Homework Handout # 5

Answers To Selected Odd-numbered Problems

1a.       Between 11 am and 5 pm, the most number of cars entering the expressway is at 2 pm (t=14).

            This is because the point (14,10.4), approximately, is an inflection point.

            Here, the function switches from concave up to concave down, and at inflection points, the rate of change is the smallest or largest.

3a.       On average, from 10:30 am to 12:30 pm, the NASDAQ is increasing by I_{[10.5, 12.5]} = 2.25 points per hour, approximately.

            On average, from 11 am to 3 pm, the NASDAQ is increasing by I_{[11, 15]} = 3.5 points per hour, approximately.

            Therefore, the NASDAQ is increasing more rapidly from 11 am to 3 pm.

3b.       The NASDAQ was increasing most rapidly at 1 pm (t=13).

            This is because the point (13, 1843), approximately, is an inflection point.

            Here, the function switches from concave up to concave down, and at inflection points, the rate of change is the smallest or largest.

5a.       Imani was burning calories most rapidly 5 minutes into her workout.

            This is because the point (5, 79), approximately, is an inflection point.

            Here, the function switches from concave up to concave down, and at inflection points, the rate of change is smallest or largest.

7a.        The number of persons receiving Social Security benefits will be increasing most rapidly in the year 2015 (t=25).

            This is because the point (25, 61), approximately, is an inflection point.

            Here, the function switches from concave up to concave down, and at inflection points, the rate of change is smallest or largest.