c. TRUE or FALSE. The tangent line for a function g(x) at the point x = a can be found using the following formula: y – g'(a) = g(a)(x – a). If true, explain why. If false give the correct formula for the tangent line at a point.
c. TRUE or FALSE. The tangent line for a function g(x) at the point x = a can be found using the following formula: y – g'(a) = g(a)(x – a). If true, explain why. If false give the correct formula for the tangent line at a point.
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:**
c. TRUE or FALSE. The tangent line for a function \( g(x) \) at the point \( x = a \) can be found using the following formula:
\[ y - g'(a) = g(a)(x - a) \]
If true, explain why. If false, give the correct formula for the tangent line at a point.
**Explanation:**
The statement is **FALSE**. The given formula is incorrect for finding the equation of the tangent line to the function \( g(x) \) at the point \( x = a \).
**Correct Formula:**
The correct formula for the tangent line to the function \( g(x) \) at the point \( x = a \) is:
\[ y - g(a) = g'(a)(x - a) \]
Where:
- \( g(a) \) is the value of the function at \( x = a \).
- \( g'(a) \) is the derivative of the function at \( x = a \), representing the slope of the tangent line.
- \( (x - a) \) indicates the horizontal displacement from the point of tangency.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31717754-3c5f-4fc1-98fe-25ebe4b28868%2F371a2972-f635-427c-8281-9b3b67374e51%2F9rpgfp_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
c. TRUE or FALSE. The tangent line for a function \( g(x) \) at the point \( x = a \) can be found using the following formula:
\[ y - g'(a) = g(a)(x - a) \]
If true, explain why. If false, give the correct formula for the tangent line at a point.
**Explanation:**
The statement is **FALSE**. The given formula is incorrect for finding the equation of the tangent line to the function \( g(x) \) at the point \( x = a \).
**Correct Formula:**
The correct formula for the tangent line to the function \( g(x) \) at the point \( x = a \) is:
\[ y - g(a) = g'(a)(x - a) \]
Where:
- \( g(a) \) is the value of the function at \( x = a \).
- \( g'(a) \) is the derivative of the function at \( x = a \), representing the slope of the tangent line.
- \( (x - a) \) indicates the horizontal displacement from the point of tangency.
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