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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Question
14
![The text from the image presents a mathematical problem:
**Problem 14:**
Given the function \( f(x) = \sqrt{8x - 3} + 7 \),
determine the value of \( x \) where the tangent line to \( f(x) \) has a slope that "Does Not Exist."
**Transcription of Solution Steps:**
1. Rewrite the function:
\[
f(x) = (8x - 3)^{\frac{1}{2}} + 7
\]
The task is to find where the derivative of the function, which represents the slope of the tangent line, does not exist. This usually occurs when the derivative involves division by zero or when the function is not differentiable at a certain point. For radical functions, such as square roots, this often happens when the expression inside the square root is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb492f7ae-3a50-4a0d-856d-c60c2ea37af5%2Fbe66d5f3-aa67-49a5-9942-6c3499b38814%2F0mip1d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The text from the image presents a mathematical problem:
**Problem 14:**
Given the function \( f(x) = \sqrt{8x - 3} + 7 \),
determine the value of \( x \) where the tangent line to \( f(x) \) has a slope that "Does Not Exist."
**Transcription of Solution Steps:**
1. Rewrite the function:
\[
f(x) = (8x - 3)^{\frac{1}{2}} + 7
\]
The task is to find where the derivative of the function, which represents the slope of the tangent line, does not exist. This usually occurs when the derivative involves division by zero or when the function is not differentiable at a certain point. For radical functions, such as square roots, this often happens when the expression inside the square root is zero.
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