* Reading Outline, Sec2.2 * ---------------------------------------- * Vocabulary/Definitions * - Difference quotient - Average rate of change of f over an interval (with respect to x) - Absolute change of a function f over an interval - Instantaneous rate of change of f at x=a - Derivative of f at a - f'(a) and slopes on the curve y = f(x) * Understand * 1. The radius, r of a cone of sand with height h = 5cm and a volume V cm^3 is r = sqrt(3V/5pi). If the volume of the cone increases from V = 7 to V = 7.15 (but the height remains constant), what is the average rate of change of the radius? 2. Estimate the derivative r'(7) for the cone above by investigating numerical values for the difference quotient.