Problem 45a
Page 189
Section 3.2: The Product and Quotient Rules
Chapter 3: Differentiation Rules
Given information
According to the question we are asked to find the value of derivative of function u(x) at x = 1, that is we have to find 
.
Now, since u(x) = f(x)g(x), that is, it is the product of two functions, therefore, we have to use the Product rule of differentiation to find the derivative of u(x).
Also, to find the functions f(x) and g(x) around x = 1, we need to find equation of lines from the graph around x = 1.
Step-by-step explanation
We observe the functions f(x) and g(x) around x = 1. From the graph for f(x) (the red curve) the equation of f(x) near x = 1 can be found as:
we use two point form to find equation of line, and the two points can be (0,0) and (1,2) (from the graph)
Using the Two point form we have:
Therefore equation of f(x) near x = 1 is f(x) = y = 2x...............(1)
Single Variable Calculus: Early Transcendentals
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