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Differentialrechnung

John Flath, Mar 1, 2017

Funktionen
1. Exponential Functions: Graphs
2. Exponential Functions (Graph & Equation Anatomy)
3. Domain & Range: Illustrated
Sekante Tangente
1. Differentiation from first principles
2. Differential calculus - first principles
Ableitung Sinus und Cosinus
1. Ableitung der Sinusfunktion
2. Ableitung der Cosinusfunktion
3. Sine & Cosine of a Sum: Discovery
4. Unit Circle and Sine Graph
Optimierung
Zweite Ableitung
1. Zusammenhang von Funktion und Ableitung
2. Zusammenhänge erste und zweite Ableitung
Kurvendiskussion

Information

Funktionen

1. Exponential Functions: Graphs
2. Exponential Functions (Graph & Equation Anatomy)
3. Domain & Range: Illustrated

Exponential Functions: Graphs

The following applet displays the graph of the exponential function

. Interact with the applet below for a few minutes, then answer the questions that follow.

Questions: 1) How does the parameter a affect the graph of the exponential function? Explain. What happens if a > 1 and k > 0? What happens if a < 1 and k > 0? 2) How does the parameter k affect the graph? Explain. If you need a hint, refer back to this worksheet. 3) What does the parameter d do the graph? Explain. 4) Suppose a < 1. Given this constraint, is it possible to get the graph of this exponential function to look the way it does when a > 1 and k > 0? Explain.