Find the equation of the tangent to the Graph. f(x)=2x² at x = 3 Step-1 Find the slope of the tangent line using the Limit Def m = Lim 0 f(3+h)-f(3) h Step-2 Find the y value when x=3 y=mx+b Solve for b (3, ?)
Find the equation of the tangent to the Graph. f(x)=2x² at x = 3 Step-1 Find the slope of the tangent line using the Limit Def m = Lim 0 f(3+h)-f(3) h Step-2 Find the y value when x=3 y=mx+b Solve for b (3, ?)
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 the Equation of the Tangent to the Graph
Given:
\[ f(x) = 2x^2 \]
at
\[ x = 3 \]
#### Step 1: Find the Slope of the Tangent Line Using the Limit Definition
The slope \( m \) is found using the following limit definition:
\[ m = \lim_{h \to 0} \frac{f(3+h) - f(3)}{h} \]
#### Step 2: Find the \( y \) Value When \( x = 3 \)
Find the point on the graph:
\[ (3, ?) \]
Using the point-slope form of the equation of a line:
\[ y = mx + b \]
Solve for \( b \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf434c73-38f1-4a89-b981-edd99d760c82%2F44a41a02-05ee-4fa9-aa22-82b72a3a61d1%2Fh9x4kde_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Equation of the Tangent to the Graph
Given:
\[ f(x) = 2x^2 \]
at
\[ x = 3 \]
#### Step 1: Find the Slope of the Tangent Line Using the Limit Definition
The slope \( m \) is found using the following limit definition:
\[ m = \lim_{h \to 0} \frac{f(3+h) - f(3)}{h} \]
#### Step 2: Find the \( y \) Value When \( x = 3 \)
Find the point on the graph:
\[ (3, ?) \]
Using the point-slope form of the equation of a line:
\[ y = mx + b \]
Solve for \( b \).
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