University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

116

Pages:

1
Author:

ardejaviwrj

Workshop #7 1. Use the definition of the derivative to complete the following. (a) Find the slope of the line that is tangent to the graph of f (x) = (b) Find the slope of the line that is tangent to the graph of f (x) = (c) Find the slope of the line that is tangent to the graph of f (x) = (d) Find the slope of the line that is tangent to the graph of f (x) = (e) Find the slope of the line that is tangent to the graph of f (x) = √ √ √ √ √ x at x = 1. x at x = 2. x at x = 3. x at x = 4. x at x = 9. 2. Use the definition of the derivative to complete the following. (a) Find the slope of the line that is tangent to the graph of f (x) = (b) Find the slope of the line that is tangent to the graph of f (x) = 1 x2 1 x2 at x = 2. at x = a. (c) Is there a point on this curve where the tangent line has slope 16? (d) Is there a point on this curve where the tangent line is horizontal? 3. Consider the graph of the hyperbola y = x1 . If you draw the tangent line at a point on the graph, it will make a triangle with a section of the x-axis and a section of the y-axis (choosing a different point results in a different triangle). Choose a point and find the area of this triangle – each person in your group should use a different point. What do you observe? Show that your observation is correct.