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The graph of f(x) is shown. At which of the point(s) is f '(x) <0 and f "(x) > 0? E A D B C

The graph of f(x) is shown. At which of the point(s) is f '(x) <0 and f "(x) > 0? E A D B C

Calculus: Early Transcendentals
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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### Graph Analysis of f(x) The graph of f(x) is shown in the provided image. The question asks: **At which of the point(s) is f '(x) < 0 and f ''(x) > 0?** Points A, B, C, D, and E are marked on the graph. ### Graph Description: - The graph depicts a function f(x), plotted on a Cartesian plane. - The x-axis is horizontal, and the y-axis is vertical. - Points A, B, C, D, and E are indicated on the graph, showing different positions of interest along the curve. #### Explanation: - **Point A:** Located at a section where the function appears to be decreasing, i.e., f '(x) < 0. - **Point B:** Positioned at a local minimum where the slope is zero, i.e., f '(x) = 0. - **Point C:** Situated in a section before the function starts increasing, i.e., f '(x) < 0. - **Point D:** Placed near the inflection point where the function transitions from concave down to concave up, i.e., f ''(x) changes from negative to positive. - **Point E:** Located in an area where the function is increasing, i.e., f '(x) > 0. ### Task: List all points where both f '(x) < 0 and f ''(x) > 0. **If there is only one point where this is true:** - List it. **If there are more than one point:** - List them all and separate the answers by commas. **If there is no such point:** - Type N. ### Sample Answer: The graph suggests that the relevant point where both conditions f '(x) < 0 and f ''(x) > 0 are met is **Point C**. **Answer: C**
Transcribed Image Text:### Graph Analysis of f(x) The graph of f(x) is shown in the provided image. The question asks: **At which of the point(s) is f '(x) < 0 and f ''(x) > 0?** Points A, B, C, D, and E are marked on the graph. ### Graph Description: - The graph depicts a function f(x), plotted on a Cartesian plane. - The x-axis is horizontal, and the y-axis is vertical. - Points A, B, C, D, and E are indicated on the graph, showing different positions of interest along the curve. #### Explanation: - **Point A:** Located at a section where the function appears to be decreasing, i.e., f '(x) < 0. - **Point B:** Positioned at a local minimum where the slope is zero, i.e., f '(x) = 0. - **Point C:** Situated in a section before the function starts increasing, i.e., f '(x) < 0. - **Point D:** Placed near the inflection point where the function transitions from concave down to concave up, i.e., f ''(x) changes from negative to positive. - **Point E:** Located in an area where the function is increasing, i.e., f '(x) > 0. ### Task: List all points where both f '(x) < 0 and f ''(x) > 0. **If there is only one point where this is true:** - List it. **If there are more than one point:** - List them all and separate the answers by commas. **If there is no such point:** - Type N. ### Sample Answer: The graph suggests that the relevant point where both conditions f '(x) < 0 and f ''(x) > 0 are met is **Point C**. **Answer: C**
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