## Practice Problems

Work through the odd-numbered problems 1-7. Once you have completed the problem set, check your answers.

### Problems

Problems 1 – 4  involve estimating slopes of tangent lines.

1) Sketch the lines tangent to the curve shown in Fig. 7 at  $x = 1, 2 \; and \; 3$.  Estimate the slope of each of the tangent lines you drew.

2) Fig. 8 shows the weight of a "typical" child from age 0 to age 24 months.  (Each of your answers should have the  units  "kilograms per month").

(a) What was the average rate of weight gain from month 0 to month 24?

(b) What was the average weight gain from month 9 to month 12?  from month 12 to month 15?

(c) Approximately how fast was the child gaining weight at age 12 months?  at age 3 months?

3) Fig. 9  shows the temperature of a cup of coffee during a ten minute period. (Each of your answers in (a) – (c) should have the units  "degrees per minute").

(a) What was the average rate of cooling from minute 0 to minute 10?

(b) What was the average rate of cooling from minute 7 to minute 8?  from minute 8 to minute 9?

(c) What was the rate of cooling at minute 8?   at minute 2?

(d) When was the cold milk added to the coffee?

4) Describe a method for determining the slope at the middle of a steep hill on campus

(a) using a ruler, a long piece of string, a glass of water and a loaf of bread.

(b) using a protractor, a piece of string and a helium–filled balloon.

Problems 5 and 6  involve approximating areas.

5) Approximate the area of the leaf in Fig. 4 .

6) Fig. 10 shows temperatures during the month of November.

(a) Approximate the shaded area between the temperature curve and the 65o line from Nov. 15 to Nov. 25.

(b) The area of the "rectangle" is (base)(height) so what are the units of your answer in part (a)?

(c) Approximate the shaded area between the temperature curve and the 65o line from Nov. 5 to Nov. 30.

(d) Who might use or care about these results?

7) Describe a method for determining the volume of a standard incandescent light bulb using a ruler, a tin coffee can, a scale, and a jug of wine.