Math: Encounters with high school students by Serge Lang

By Serge Lang

Dieses Buch enthalt eine Sammlung von Dialogen des bekannten Mathematikers Serge Lang mit Schulern. Serge Lang behandelt die Schuler als seinesgleichen und zeigt ihnen mit dem ihm eigenen lebendigen Stil etwas vom Wesen des mathematischen Denkens. Die Begegnungen zwischen Lang und den Schulern sind nach Bandaufnahmen aufgezeichnet worden und daher authentisch und lebendig. Das Buch stellt einen frischen und neuartigen Ansatz fur Lehren, Lernen und Genuss von Mathematik vor. Das Buch ist von grossem Interesse fur Lehrer und Schule

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If f ͑x͒ ෇ x2 Ϫ x xϪ1 and (c) (d) (e) (f) Estimate the solution of the equation f ͑x͒ ෇ Ϫ1. On what interval is f decreasing? State the domain and range of f. State the domain and range of t. t͑x͒ ෇ x is it true that f ෇ t? y g f 3. The graph of a function f is given. (a) (b) (c) (d) (e) (f) whenever x 1 Ͻ x 2 in I State the value of f ͑1͒. Estimate the value of f ͑Ϫ1͒. For what values of x is f ͑x͒ ෇ 1? Estimate the value of x such that f ͑x͒ ෇ 0. State the domain and range of f. On what interval is f increasing?

Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 1 y D The graph shown in Figure 22 rises from A to B, falls from B to C , and rises again from C to D. The function f is said to be increasing on the interval ͓a, b͔, decreasing on ͓b, c͔, and increasing again on ͓c, d͔. Notice that if x 1 and x 2 are any two numbers between a and b with x 1 Ͻ x 2 , then f ͑x 1 ͒ Ͻ f ͑x 2 ͒. We use this as the defining property of an increasing function.

Velocity When we look at the speedometer of a car and read that the car is traveling at 48 mi͞h, what does that information indicate to us? We know that if the velocity remains constant, then after an hour we will have traveled 48 mi. But if the velocity of the car varies, what does it mean to say that the velocity at a given instant is 48 mi͞h? In order to analyze this question, let’s examine the motion of a car that travels along a straight road and assume that we can measure the distance traveled by the car (in feet) at l-second intervals as in the following chart: t ෇ Time elapsed (s) 0 1 2 3 4 5 d ෇ Distance (ft) 0 2 9 24 42 71 Copyright 2010 Cengage Learning.

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