Find f'(x) Find f(2) Find f'(2) Write the equation of the tangent line at x=2

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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f(x)=3x2-4x+7

The image presents a series of mathematical tasks related to calculus. The tasks are as follows:

1. **Find f'(x)**: This involves calculating the derivative of the function f with respect to x, denoted as f'(x). The derivative represents the rate of change of the function at any given point x.

2. **Find f(2)**: This requires evaluating the function f at x = 2. Essentially, it means substituting x = 2 into the function to determine the corresponding y-value or output.

3. **Find f'(2)**: This involves computing the derivative of the function at the specific point where x = 2. It represents the slope of the tangent line to the function at x = 2.

4. **Write the equation of the tangent line at x=2**: This task requires finding the equation of the line that just touches the curve of function f at x = 2. This involves using the point-slope form of the equation of a line, employing the point (2, f(2)) and the slope f'(2).

There are no graphs or diagrams accompanying the text.
Transcribed Image Text:The image presents a series of mathematical tasks related to calculus. The tasks are as follows: 1. **Find f'(x)**: This involves calculating the derivative of the function f with respect to x, denoted as f'(x). The derivative represents the rate of change of the function at any given point x. 2. **Find f(2)**: This requires evaluating the function f at x = 2. Essentially, it means substituting x = 2 into the function to determine the corresponding y-value or output. 3. **Find f'(2)**: This involves computing the derivative of the function at the specific point where x = 2. It represents the slope of the tangent line to the function at x = 2. 4. **Write the equation of the tangent line at x=2**: This task requires finding the equation of the line that just touches the curve of function f at x = 2. This involves using the point-slope form of the equation of a line, employing the point (2, f(2)) and the slope f'(2). There are no graphs or diagrams accompanying the text.
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