Chapter 3.01
On #6-11, don't bother simplifying your answer. If you get something like 3*5,
just leave it as 3*5.

Remember that you should be graphing each function and its derivative, and
visually checking that the derivative graph makes sense. This is for two
reasons:
* it helps you check your formula-based work, thus helping you give yourself
feedback on how you are doing on formula skills.
* it helps build your intuition on how a graph looks in relation to its
derivative. This is valuable on its own, and is also valuable as a reverse
skill when we get to doing integrals.
 4
 5
 6

 8
 9

 11
 12
 13

 15

 16

 18

 20
 21

 26
 28

 31
 32
 33 WEP
 34
 35
 36 WEP
 37 WEP
 38 WEP
 39
 407
 41 WEP
 42 WEP
 43
 44
 45
 46 WEP
 47
 49 (note they got Boyle's Law a little wrong: it assumes constant
 temperature, not constant pressure)
 50 WEP
 51 WEP
 52 

 61 MTH/MTHT
 62 MTH/MTHT
 63 

 QA: Let f(x) = x*(2-x) if x>=0, or x*(x+2) if x<0
 i) graph the function from x=-3 to x=+3
 ii) Find and graph its derivative
 iii) Find and graph its 2nd derivative 

 QB: Let f(x) = (x+2)*(x)*(x-2)/-3.08
 i) graph the function from x=-3 to x=+3
 ii) Find and graph its derivative
 iii) Find and graph its 2nd derivative 
 iv) Compare to the results in QA.

 QC:
 i) The volume of a sphere with radius r is (4/3)*pi*r^3. The derivative with
 respect to r is ____, which by coincidence (?) is the formula for _________.
 ii) The area of a circle with radius r is pi*r^2. The derivative with respect
 to r is ____, which by coincidence (?) is the formula for _________.
 iii) The area of a square with lower-left corner at (-x,-x) and upper-right
 corner at (x,x) is (2x)^2; the derivative with respect to x is __________,
 and is that the formula for the perimeter of that square?
 iv) optional: what if we measure the width of the square along the diagonal
 rather than perpendicular to the sides?

 QD:
 The derivative of a cubic is a _________.
 The derivative of a parabola is a ________.
 The derivative of a straight line is a ________.
 The derivative of a horizontal line is a ________.

 QE: The Lennard-Jones potential function approximates the force between two
 neutral atoms at a distance r>0 from each other. It is
 f(r) = k*( (s/r)^12 - (s/r)^6 )
 where k and s are positive physical constants. We will use k=1 and s=2.
 i) Graph f(r) for r between 1.5 and 4
 ii) find f'(r) and graph it, also between r=1.5 and 4.

The "Applied Project" about "Building a Better Roller Coaster" might be a
good project for some people in our class. Skim through it and see if you 
are interested.