23 Dec 2021
Problem 53
Page 190
Section 3.2: The Product and Quotient Rules
Chapter 3: Differentiation Rules
Textbook ExpertVerified Tutor
23 Dec 2021
Given information
given that a tangent line at 
has equation 
Step-by-step explanation
Step 1.
The question is to find how many tangent lines to the given curve passes through the given point Also, we need to find at which points do these tangent tines touch the curve.
The form of the tangent line through the point and with slope 
is
and with slope is
We know that the slope of a tangent at any point is the derivative at that point.
Applying The Quotient Rule :
If 
and 
are differentiable, then
and are differentiable, then
we obtain
Therefore,
Substituting this in equation (1), follows
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 42b
- Problem 42c
- Problem 42d
- Problem 44
- Problem 45a
- Problem 45b
- Problem 47a
- Problem 47b
- Problem 47c
- Problem 48a
- Problem 48d
- Problem 49
- Problem 50a
- Problem 50b
- Problem 51
- Problem 53
- Problem 54
- Problem 55
- Problem 56
- Problem 57b
- Problem 60b