Work through the odd-numbered problems 1-37. Once you have completed the problem set, check your answers.
(e) DNE
(f) DNE
13. For any constant , if , then
The graphs of and are "parallel" parabolas: is shifted up 3 units, and is shifted
down 5 units.
15. . Then and the equation of the tangent line at is or .
and the equation of the tangent line at is or .
17. . Then and the equation of the tangent line at is or .
and the equation of the tangent line at is or .
(c) so the tangent line is horizontal when : at the point .
(d) (the slope of the tangent line) so or .
Since , the equation of the tangent line becomes .
(e) We need such that . Then . There are two points with the
property we want: and .
21. (a) , so when . Angle radians .
(b) , so when . Angle radians .
(c) Angle radians radians (or angle )
23. Graph. On the graph of upward velocity, the units on the horizontal axis are "seconds" and the units on the vertical axis are "feet per second".
25. (a) ft. ft. (b) ft/sec ft/sec.
27. dollars to produce golf balls.
Marginal production cost is dollars per golf ball. dollars per golf ball. dollars per golf ball.
29.
(d) represents the rate at which is increasing, the rate at which area is accumulating.
31 .