• Monday. Quiz on quotient rule. More on graphing. Product
rule for more

than two functions. Derivatives of radicals - part one.

Homework.

1. A function has vertical asymptotes x=1 and x=-3. It
passes thru

(0,4). The derivative is negative when x < 0 and positive when

x > 0. Sketch a graph of this function. What can you tell me about

the derivative of the function?

2. Sketch the graph of

3. p 283 #7

4. p 284 #11

5. p 119 #5

6. p 120 #15

7. p 166 #7 , 18

8. p 155 #23-42 work the ones with a square root.

9. p 155 #47

• Tuesday. Quiz on graphing rational functions. More on
the derivative of

radicals and roots - back to the power rule! Composition of functions.

Homework.

1. p 262 #47 (This is like the first few days of class.)

2. p 262 # 51

3. Sketch the graph of f(x) =

4. Sketch the graph of g(x) =

5. p 284 #9

6. Find the maximum and minimum of f(x) = 3x^2 - 12x + 5 on the

interval [0, 3] (0 ≤ x ≤ 3).

7. page 166 #10

8. p 155 #53

9. p155 #58 (a-c)

Wednesday. Graphing quiz? Today we will focus on the chain
rule. What

is it and how is it used?

Homework.

1. p 181 #3

2. p 181 #7-10

3. p 210 #5 (Linearization means the best straight line to approximate

the function - what we called the tangent line!)

4. p262 #49

5. Sketch the graph of Use the derivative and
information

about asymptotes, etc.

6. p 284 #10

7. Use the slope/tangent line to approximate
Check your answer

by cubing your result. If we did 8.2 instead of 8.1, how would this

change your answer? So, for each increase of x by 0.1, the cube root

of x will increase by (approximately) how much? (Only for x near 8,

of course.)

Thursday. Review of chain rule. Application of tangents.
Newton's Method

for (approximately) solving equations { bring your calculators!!!

Homework.

1. p181 #25, 39 (Chain rule review)

2. p181 #43 (Review tangents and chain rule.)

3. p 210 #9 (Review tangents.)

4. p231 # 51 (Review max/min)

5. p 284 #15 (Application. Use the distance formula (see inside, front

cover) and use fact that one point is (0,0) and the other is (x, 4x+7).

Write out the distance and then take derivative. Feel free to use the

calculator to compute derivative.)

6. p 182 #59 (Chain rule - see problem in notes.)

7. Page 298 #1 (Draw a picture with tangents and use to approximate

the roots - using the geometric picture behind Newton's method.)

8. page 298 #5,9 (Do not use the calculator 'tricks' from class. Start

with newroot = x - f(x)/f'(x) and plug in your values.)

9. p298 #13 Now use the calculator tricks from class. Continue iterating

until the solution remains constant in the sixth decimal place. (Place

function into y = menu, for y1. Then at home screen enter a -

f(a)/f'(a)|a = 2. After evaluating replace a = 2 by a = ans.)

Friday. We will review. I have some material and then I
plan on breaking

the class into groups and have each group explain a homework problem. Be

prepared to participate - I want to get a better feeling for where everyone

is at before we move on.

Homework. (some may look familiar - I wanted to see if you
could do these,

of if you are just not asking questions. I plan to have group presentations

again on Monday.)

1. Sketch the graph of g(x) =

2. Find the point on the graph of y = 1/x+1, that is nearest the point

(5, 5). Start by looking at the graph and making a guess, then set

up an equation and minimize. Be sure that your final answer agrees

(somewhat) with your guess.

3. Use the slope/tangent line to approximate
Check your answer

by cubing your result. If we did 8.2 instead of 8.1, how would this

change your answer? So, for each increase of x by 0.1, the cube root

of x will increase by (approximately) how much? (Only for x near 8,

of course.)

4. A box with an open top and a rectangular base with length twice the

width must have a volume of 32,000 cubic inches. Find the dimen-

sions of the box to minimize the material used.

5. Sketch the graph of

6. Sketch the graph of

7. Sketch a function f that satisfies all of the following.

f'(2) = 0, f'(0) = 1,f'(x) > 0, if 0 < x < 2,

f'(x) < 0, if x > 2,, as x gets large, f(x) gets very small,

and f(x) = -f(-x).