Let y=f(x) = 4x^2/4x+1 d) Find the equation of the tangent line to the curve y=f(x) at the point x=1  (e) Use your answer in (d) to approximate f(1.01) without using a calculator.

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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Let y=f(x) = 4x^2/4x+1

d) Find the equation of the tangent line to the curve y=f(x) at the point x=1

 (e) Use your answer in (d) to approximate f(1.01) without using a calculator.

 

Certainly! 

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**Function Definition:**

Let \( y = f(x) = \frac{4x^2}{4x + 1} \)

This function represents a rational expression where the numerator is a quadratic term \( 4x^2 \), and the denominator is a linear term \( 4x + 1 \).

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Feel free to incorporate this transcription into your educational materials.
Transcribed Image Text:Certainly! --- **Function Definition:** Let \( y = f(x) = \frac{4x^2}{4x + 1} \) This function represents a rational expression where the numerator is a quadratic term \( 4x^2 \), and the denominator is a linear term \( 4x + 1 \). --- Feel free to incorporate this transcription into your educational materials.
(d) Find the equation of the tangent line to the curve \( y = f(x) \) at the point \( x = 1 \).

(e) Use your answer in (d) to approximate \( f(1.01) \) without using a calculator.
Transcribed Image Text:(d) Find the equation of the tangent line to the curve \( y = f(x) \) at the point \( x = 1 \). (e) Use your answer in (d) to approximate \( f(1.01) \) without using a calculator.
Expert Solution
Step 1

Equation of tangent to the curve y=f(x) at a point x=a is y-f(a)=f'(a)(x-a)

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