## Practice Problems

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 slope of 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. Graph and . Calculate the derivatives of , , and .

In problems 15 – 17, find the slopes and equations of the lines tangent to at the given points.

19. (a) Find the equation of the line tangent to the graph of at the point .

(b) Find the equation of the line perpendicular to the graph of at .

(c) Where is the tangent to the graph of horizontal?

(d) Find the equation of the line tangent to the graph of at the point .

(e) Find the point(s) on the graph of so the tangent line to the curve at goes through the point .

21. (a) Find the angle that the tangent line to at makes with the x–axis.

(b) Find the angle that the tangent line to at makes with the x–axis.

(c) The curves and intersect at the point . Find the angle of intersection of the two curves (actually the angle between their tangent lines) at the point .

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 drop feet 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 to be the area bounded by the x–axis, the line , and a vertical line at (Fig. 15).

(b) Find a formula which represents for all ?

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

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