Find an equation of the line that is tangent to the graph of fand parallel to the given line. Function Line f{x) = x²|4x – y + 4 = 0 STEP 1: Find f '(x) using the limit definition of the derivative. f "(x) = STEP 2: Find the slope m of the given line. m = STEP 3: Equate f '(x) with the slope and solve for x. STEP 4: Find the corresponding y value by substituting x into f(x). At the point (x, y) = (| ] ) the tangent line of f(x) is parallel to 4x – y + 4 = 0. STEP 5: Use the results of Step 2 and Step 4 with the point-slope formula to find the equation of the line. y =
Find an equation of the line that is tangent to the graph of fand parallel to the given line. Function Line f{x) = x²|4x – y + 4 = 0 STEP 1: Find f '(x) using the limit definition of the derivative. f "(x) = STEP 2: Find the slope m of the given line. m = STEP 3: Equate f '(x) with the slope and solve for x. STEP 4: Find the corresponding y value by substituting x into f(x). At the point (x, y) = (| ] ) the tangent line of f(x) is parallel to 4x – y + 4 = 0. STEP 5: Use the results of Step 2 and Step 4 with the point-slope formula to find the equation of the line. y =
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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![**Finding an Equation of a Tangent Line**
This section will guide you through the steps necessary to find an equation of the line that is tangent to the graph of a given function \(f\) and parallel to a provided line.
**Function and Line Information:**
\[
\begin{array}{|c|c|}
\hline
\text{Function} & \text{Line} \\
\hline
f(x) = x^2 & 4x - y + 4 = 0 \\
\hline
\end{array}
\]
**Step-by-Step Procedure:**
**STEP 1:**
Find \( f' (x) \) using the limit definition of the derivative.
\[
f' (x) = \_\_\_\_\_
\]
**STEP 2:**
Find the slope \( m \) of the given line.
\[
m = \_\_\_\_\_
\]
**STEP 3:**
Equate \( f' (x) \) with the slope and solve for \( x \).
\[
x = \_\_\_\_\_
\]
**STEP 4:**
Find the corresponding \( y \) value by substituting \( x \) into \( f(x) \).
At the point \( (x, y) = \left( \_\_\_\_\_, \_\_\_\_\_ \right) \) the tangent line of \( f(x) \) is parallel to \( 4x - y + 4 = 0 \).
**STEP 5:**
Use the results of Step 2 and Step 4 with the point-slope formula to find the equation of the line.
\[
y = \_\_\_\_\_
\]
These steps systematically show how to derive the equation of a tangent line to a given function that is parallel to a specific line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc550f2c8-5f01-4988-ace5-8dc585de8201%2Ff940314e-e3ac-480c-af11-05247cbc2e27%2Fk1iilkj.png&w=3840&q=75)
Transcribed Image Text:**Finding an Equation of a Tangent Line**
This section will guide you through the steps necessary to find an equation of the line that is tangent to the graph of a given function \(f\) and parallel to a provided line.
**Function and Line Information:**
\[
\begin{array}{|c|c|}
\hline
\text{Function} & \text{Line} \\
\hline
f(x) = x^2 & 4x - y + 4 = 0 \\
\hline
\end{array}
\]
**Step-by-Step Procedure:**
**STEP 1:**
Find \( f' (x) \) using the limit definition of the derivative.
\[
f' (x) = \_\_\_\_\_
\]
**STEP 2:**
Find the slope \( m \) of the given line.
\[
m = \_\_\_\_\_
\]
**STEP 3:**
Equate \( f' (x) \) with the slope and solve for \( x \).
\[
x = \_\_\_\_\_
\]
**STEP 4:**
Find the corresponding \( y \) value by substituting \( x \) into \( f(x) \).
At the point \( (x, y) = \left( \_\_\_\_\_, \_\_\_\_\_ \right) \) the tangent line of \( f(x) \) is parallel to \( 4x - y + 4 = 0 \).
**STEP 5:**
Use the results of Step 2 and Step 4 with the point-slope formula to find the equation of the line.
\[
y = \_\_\_\_\_
\]
These steps systematically show how to derive the equation of a tangent line to a given function that is parallel to a specific line.
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