Use the graph of f below to answer the question. Assume that the domain of f is (−∞,∞). At which x-values does a local maximum of f occur? x=0 x=1 x=2 x=3 x=4 x=5

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use the graph of f below to answer the question. Assume that the domain of f is (−∞,∞).

At which x-values does a local maximum of f occur?

  • x=0
  • x=1
  • x=2
  • x=3
  • x=4
  • x=5
The image displays a graph of a function on a Cartesian coordinate system. 

### Key Features of the Graph:

1. **Axes**:
   - The horizontal axis is labeled as \(x\), ranging from \(-1\) to \(6\).
   - The vertical axis is labeled as \(y\), ranging from \(-1\) to \(6\).

2. **Curve**:
   - The graph is a smooth, continuous blue curve with several key points:
     - Starts from above \(y = 5\) at \(x = -1\).
     - Decreases steeply, reaching its first local minimum just above \(y = 1\) near \(x = 1\).
     - Increases again, reaching a local maximum slightly above \(y = 3\) around \(x = 2.5\).
     - Then decreases to a local minimum close to \(y = 1\) near \(x = 5\).
     - Slightly increases as it approaches \(x = 6\).

3. **Grid and Scale**:
   - The background features a grid pattern that helps in identifying the position of points.
   - Both axes are evenly numbered to aid in interpreting the graph's features.

This graph can be used to discuss concepts such as local maxima and minima, intervals of increase and decrease, and the smooth, continuous nature of the function. It provides a clear visual representation to aid in the understanding of these mathematical concepts.
Transcribed Image Text:The image displays a graph of a function on a Cartesian coordinate system. ### Key Features of the Graph: 1. **Axes**: - The horizontal axis is labeled as \(x\), ranging from \(-1\) to \(6\). - The vertical axis is labeled as \(y\), ranging from \(-1\) to \(6\). 2. **Curve**: - The graph is a smooth, continuous blue curve with several key points: - Starts from above \(y = 5\) at \(x = -1\). - Decreases steeply, reaching its first local minimum just above \(y = 1\) near \(x = 1\). - Increases again, reaching a local maximum slightly above \(y = 3\) around \(x = 2.5\). - Then decreases to a local minimum close to \(y = 1\) near \(x = 5\). - Slightly increases as it approaches \(x = 6\). 3. **Grid and Scale**: - The background features a grid pattern that helps in identifying the position of points. - Both axes are evenly numbered to aid in interpreting the graph's features. This graph can be used to discuss concepts such as local maxima and minima, intervals of increase and decrease, and the smooth, continuous nature of the function. It provides a clear visual representation to aid in the understanding of these mathematical concepts.
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