In Problems 31 and 32, a graph is given. Tell where f(x) is concave up, where it is concave down, and where it has points of inflection on the interval -2

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Question 32

**Transcription for Educational Website**

### In Problems 31 and 32
A graph is given. Identify where \( f(x) \) is concave up, where it is concave down, and where it has points of inflection on the interval \(-2 < x < 2\) if the given graph is the graph of:

- (a) \( f(x) \)
- (b) \( f'(x) \)
- (c) \( f''(x) \)

#### Problem 31
Graph Explanation: 
- A graph with key points on the coordinate plane.

#### Problem 32
Graph Explanation: 
- A graph with key points on the coordinate plane.

### Applications

#### 33. Productivity—Diminishing Returns
The figure depicts a typical graph of worker productivity as a function of time on the job.

**Graph Description:**
- The horizontal axis represents time (\( t \)).
- The vertical axis represents productivity (\( P \)).
- The curve starts at point \( A \) and increases, showing productivity gains. Over time, the curve flattens as it approaches a dashed line at point \( C \), indicating diminishing returns.

#### Details:
- The horizontal line from points \( B \) to \( C \) indicates the maximum productivity level.

**Tasks:**
(a) If \( P \) represents the productivity and \( t \) represents the time, write a mathematical symbol that represents the limit of productivity with respect to time.

(Note: The summary is based on the visible content in the image.)
Transcribed Image Text:**Transcription for Educational Website** ### In Problems 31 and 32 A graph is given. Identify where \( f(x) \) is concave up, where it is concave down, and where it has points of inflection on the interval \(-2 < x < 2\) if the given graph is the graph of: - (a) \( f(x) \) - (b) \( f'(x) \) - (c) \( f''(x) \) #### Problem 31 Graph Explanation: - A graph with key points on the coordinate plane. #### Problem 32 Graph Explanation: - A graph with key points on the coordinate plane. ### Applications #### 33. Productivity—Diminishing Returns The figure depicts a typical graph of worker productivity as a function of time on the job. **Graph Description:** - The horizontal axis represents time (\( t \)). - The vertical axis represents productivity (\( P \)). - The curve starts at point \( A \) and increases, showing productivity gains. Over time, the curve flattens as it approaches a dashed line at point \( C \), indicating diminishing returns. #### Details: - The horizontal line from points \( B \) to \( C \) indicates the maximum productivity level. **Tasks:** (a) If \( P \) represents the productivity and \( t \) represents the time, write a mathematical symbol that represents the limit of productivity with respect to time. (Note: The summary is based on the visible content in the image.)
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