Page 2: Advanced Kurvendiskussion Examples

This page continues with more complex e-Funktion Kurvendiskussion examples. It analyzes the functions f(x) = x • e^-x and f(x) = (x-2) • ex.

For each function, the analysis includes:

• Checking for symmetry
• Calculating limits for extreme values of x
• Finding zeros and y-intercepts
• Deriving first, second, and third derivatives
• Locating extrema and inflection points
• Sketching the graph based on the analysis

The page emphasizes the importance of considering both positive and negative infinity when analyzing asymptotic behavior of exponential functions.

Example: For f(x) = x • e^-x, the analysis shows it has a maximum point at (-1, 0.368) and an inflection point at (2, 0.368).

Highlight: The page demonstrates how to use the Krümmungsverhalten e-Funktion (curvature behavior) to determine the nature of critical points.

Page 3: Complex E-Function Analysis

This page delves into more advanced e-Funktion Kurvendiskussion problems. It analyzes two complex functions: f(x) = e^-x² and f(x) = (x²-3x) • ex.

For f(x) = e^-x², the analysis includes:

• Identifying axis symmetry
• Calculating limits
• Proving there are no real zeros
• Finding derivatives up to the third order
• Locating extrema and inflection points

The analysis of f(x) = (x²-3x) • ex is more intricate, covering:

• Lack of symmetry
• Limit calculations
• Finding multiple zeros
• Deriving complex expressions for derivatives
• Solving for extrema and inflection points using advanced techniques

Vocabulary: Wendepunkt - inflection point in German mathematical terminology.

Highlight: The page demonstrates how to handle zusammengesetzte Funktionen (composite functions) in Kurvendiskussion e-Funktion Aufgaben.