Math 191           Study Guide for Hour Quiz #2 on Chapter 3            C.S.Davis

Your are responsible for the subject matter in Chapter 3. The following topics and exercises are central in their importance. I have assigned a minimal number of exercises at the end of each topic from Calculus, by James Stewart,6^th ed. . Work more similar exercises if you need to do so in order to master the topics.

3.1

1.

Define derivative of a function f at a number a. Text

2.

Sketch a graph of a function given a few values of f(x) and f’(x) (connect the dots and dashes". P120#19

3.

Find the equation of the secant line to a curve given the two x-values where the secant line crosses the curve. P119#1

Find the equation of the tangent line to a curve given the the x-value where the tangent line touches the curve. P119#3

4.

Find f ’(a) using the definition of derivative (algebraically). P121#25

5.

Find the equation of the tangent line at a given point and show its graph matches the graph of the function if you zoom in enough. P121#21

3.2

1.

Define derivative of a function f. Text

2.

Use the various notations for derivative. Text

3.

Calculate the derivative by the definition (taking the limit of a difference quotient). P132#21,23,25

4.

Give a geometric example of a function whose derivative exists at some points and does not exist at others. Include examples of corners, cusps, vertical tangents and discontinuities (removable, jump and infinite). P133#33

5.

Given the graph of y = f(x), draw the graph of y' = f'(x). P131#1,3,5,7,9,11

6.

Given a t-table of x and f(x) values, estimate a column of f’(x) values. P133#31

3.3

1.

Apply the rules (theorems) of differentiation: sum, difference, product, quotient, power, constant factor. P144#3,9,11,15,19,21,23,27,33,37,39

2.

Calculate the slope and equation of the tangent line and graph it and the function on the same screen.  Zoom in until they match. P144#51,53

3.4

1.

Take derivatives involving trig functions. P154#1,5,9,15,17

2.

Find limits involving trig functions. P155#39,42,44

3.5

1.

Apply the chain rule in both popular forms:

a.

using the composite function: (f B g)'(x) = f '(g(x))·g'(x)

b.

using the names of the variables: dy/dx = dy/du·du/dx P161#1-33 odd

3.6

1.

Differentiate implicitly. P169#5,9,15,17,19

2.

Find the equation of the tangent line to a curve at a given value of (x,y). (Again) P169#29

1.

Find the equation of the secant line to a curve given the two x-values where the secant line crosses the curve.

Find the equation of the tangent line to a curve given the the x-value where the tangent line touches the curve. P132#7

2.

Find the average velocity of an object in motion given two times.

Find the instantaneous velocity of an object in motion at a given time.   P179#1,5,9

3.

Find the average rate of change of a quantity y = f(x) with respect to x at a given two values of x.

.

Find the instantaneous rate of change of a quantity y = f(x) with respect to x at a given value of x. P180#15

3.8

1.

Solve a related rates word problem involving

a.

sides of right triangles. P187#13,15

b.

areas of right triangles, rectangles and circles. P188#29

c.

volumes of rectangular solids, cylinders, cones and spheres. P188#1,27

3.9

1.

Give the linearization of a function and use it to approximate the function. P193#1,41

2.

Draw a diagram depicting and describe dx, delta x, dy and delta y for a function f.   P192#19

3.

Calculate differentials. P193#11,15

4.

Solve a word problem involving differentials. P194#31

Maple Computer Assignment: DiffQuot.mws