7. Given the graph of a differentiable function f(x), we would like to calculate the length of the curve in the graph. (For example the length of the curve in the figure to Problem 1.) (a) If you had a piece of string and a ruler, how could you determine the length of the curve? (b) Suppose you only had a ruler, how could we determine the length? Is this precise or an approxi- mation? (c) Suppose we only have the coordinate axes, not a ruler and no string. How could we then approx- imate the length? This should involve the Pythagorean Theorem, a sum and differentials. (d) How could we improve the accuracy of our estimate? What would be the most precise answer?

5.) y=500/[1 + 24e(-.26t)] with an inflection point at t=12.2 Sketch the graph and its inflection point

ApPplications for. For each function and graph in Problems 21, 22, 23, and 24 Cover Page a. use the graph to identify æ-values for which / > 0, y < 0, y = 0, and y does not exist. Title Page b. use the derivative to check your conclusions. Copyright Page 21. y = 6 – x – x² Preface Acknowledgments xiv 4+ 0. Algebraic Concepts -6 1. Linear Equations and 52 -8+ Functions

11. Question: If you also knew that the function was concave down at the point (5, –1) what type of increasing/decreasing behavior would the function have at x = 5?