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Use differentials and the graph of g' to approximate the following, given that g(3) = 4. %3D places.) 3 5 (3, –4) (a) g(2.93) 8.035 (b) g(3.1) 7.95 4. 2. 2.

Use differentials and the graph of g' to approximate the following, given that g(3) = 4. %3D places.) 3 5 (3, –4) (a) g(2.93) 8.035 (b) g(3.1) 7.95 4. 2. 2.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Using Differentials and Graphs to Approximate Values **Task:** Use differentials and the graph of \( g' \) to approximate the given values, with the information that \( g(3) = 4 \). Round your answers to three decimal places. #### Graph Description: The graph depicted is a curve labeled \( g' \), representing the derivative of a function \( g \). The graph features a point of interest at \( (3, -\frac{1}{2}) \), indicating the slope of the function at \( x = 3 \). The curve is shown decreasing, primarily in the first quadrant, with recognizable points around the x-axis from 1 to 5 and the y-axis up to 4. #### Approximation Tasks: - **(a) Approximating \( g(2.93) \)** Estimated Value: 8.035 ✗ (Incorrect) - **(b) Approximating \( g(3.1) \)** Estimated Value: 7.95 ✗ (Incorrect) Note: The wrong estimates suggest a need for closer inspection and method adjustment. When using differentials for approximation, ensure calculations align with the derivative's behavior intensely observed at the point of interest.
Transcribed Image Text:### Using Differentials and Graphs to Approximate Values **Task:** Use differentials and the graph of \( g' \) to approximate the given values, with the information that \( g(3) = 4 \). Round your answers to three decimal places. #### Graph Description: The graph depicted is a curve labeled \( g' \), representing the derivative of a function \( g \). The graph features a point of interest at \( (3, -\frac{1}{2}) \), indicating the slope of the function at \( x = 3 \). The curve is shown decreasing, primarily in the first quadrant, with recognizable points around the x-axis from 1 to 5 and the y-axis up to 4. #### Approximation Tasks: - **(a) Approximating \( g(2.93) \)** Estimated Value: 8.035 ✗ (Incorrect) - **(b) Approximating \( g(3.1) \)** Estimated Value: 7.95 ✗ (Incorrect) Note: The wrong estimates suggest a need for closer inspection and method adjustment. When using differentials for approximation, ensure calculations align with the derivative's behavior intensely observed at the point of interest.
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