Work through the odd-numbered problems 1-37. Once you have completed the problem set, check your answers.
1. Match the graphs of the three functions in Fig. 8 with the graphs of their derivatives.
In problems 3-5, find the slopeof the secant line through the two given points and then calculate .
7. Use the graph in Fig. 10 to estimate the values of these limits. (It helps to recognize what the limit represents.)
In problems 9 – 11, use the Definition of the derivative to calculate and then evaluate .
13. Graphand . Calculate the derivatives of , , and .
In problems 15 – 17, find the slopes and equations of the lines tangent toat the given points.
19. (a) Find the equation of the line tangent to the graph ofat the point .
(b) Find the equation of the line perpendicular to the graph ofat .
(c) Where is the tangent to the graph ofhorizontal?
(d) Find the equation of the line tangent to the graph ofat the point .
(e) Find the point(s) the point
21. (a) Find the angle that the tangent line toat makes with the x–axis.
(b) Find the angle that the tangent line toat makes with the x–axis.
(c) The curves curves (actually the angle between their tangent lines) at the point .and intersect at the point . Find the angle of intersection of the two
23. Fig. 13 shows the graph of the height of an object at time . Sketch the graph of the object's upward velocity. What are the units for each axis on the velocity graph?
25. A rock dropped into a deep hole will dropfeet in seconds.
(a) How far into the hole will the rock be after 4 seconds? 5 seconds?
(b) How fast will it be falling at exactly 4 seconds? 5 seconds?seconds?
27. It costs dollars to produce golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when ? when ? (Include units.)
29. Define the line , and a vertical line at (Fig. 15).to be the area bounded by the x–axis,
(a) Evaluate and .
(b) Find a formula which represents for all ?
(d) What does represent?
31. Find (a)
In problems 31 – 37, find a function which has the given derivative. (Each problem has several correct answers, just find one of them.)
Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-3.2-Definition-of-Derivative.pdf
This work is licensed under a Creative Commons Attribution 3.0 License.