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)