More applications for derivatives

Note:  The sheet of extra problems was from the book: p.185/52;  p.193/36, 39, 40, 50, 51

We are starting to get into the actual applications of derivatives.

10/26  4.3  Using derivatives to graph
                  HW p.204-206/8-29 by 3's, 31-39 odd, 41-48
10/27  4.4  Optimization (derivatives to find min/max)
                  HW p.214-217/1,5,7,9,15,17,20,22,25,26,28,32,34,36
10/28  4.4  AP Problem Quiz
                  HW p.217-219/39-43, 45, 47, 49
10/29  4.5  Linear Approximations (using a different book!)
                  HW HH/1-10, 14-17  and  p.229-231/11-14, 52

11/02  4.5  Using the approximation
                  HW HH/11-13  and  p.230-231/31-45 odd
11/03  8.1  L'Hopital's Rule (derivatives to find limits)
                  HW p.423-425/1-47 odd, 50, 52
11/04  4.6  Quick Quiz;  Related Rates (everything depends on t)
                  HW p.237-239/3, 5, 6, 9, 11-13, 15, 18-22, 24
11/05  4.6  More Related Rates (because everything depends on t)
                  HW p.240-241/27, 28, 30, 32, 34, 35, 37, 39, 40, 41

11/09  Review and extra questions
11/10  Ch. 4 Test
                   HW Enter RAM program in calculator, p.229-231/16-18, 50, 51
11/11  Veterans Day - no school

Starting Derivative Applications (Ch 4)

The first two sections of Chapter 4 mesh together so the homework will be a bit back-and-forth.

10/21  p.192-193/3, 5, 9, 13, 15-20, 21a, 24a, 25-33 odd
10/22  p.184-185/27-35 odd, 36, 37-43  odd, 45-51 plus a sheet of extras

Answers to today's extra questions

1.  For the ellipse problem today (4x^2 + 9y^2 = 36) with the generic first quadrant point (p, q), you should find the following:

xT = 9/p
yT = 4/q
xN = 5p/9
yN = -5q/4

Given that p goes from 0 to 3 and q goes from 0 to 2, we can say the following about possible values of the tangent and normal intercepts:

xT = (3, infinity)
yT = (2, infinity)
xN = (0, 5/3)
yN = (-5/2, 0)

2.  For e^(2x) = k*sqrt(x) then it happens at x = 1/4 when k = 2/sqrt(e
(if you need a hint, you have two equations (original and slopes) for the two unknowns (k and x))

More with Derivatives

Here is the syllabus for the rest of the chapter.  

Please note that the homework after the Chain Rule class is slightly different from that posted on the board!

10/06  3.6 Chain Rule (some more)
            HW p.147-148/33-39 odd, 57, 58, 60-65, 68, 71
10/07  3.7 Implicit Differentiation
            HW p.155-156/3, 7, 11-37 odd, 40-45
10/08  3.7 Prove power rule for rational powers  HW p.156-157/46-51
            3.8 Derivatives of Inverse Trig Functions  
             HW p.162-163/1-19 by 3's,20,21-33 odd,34

10/12  Columbus Day, no school
10/13  3.9  Derivatives of Exp and Log Functions  
            HW p.170-171/1-41 alternating odds,42,47-50,52
10/14  Professional Development - no school
10/15  3.9 Logarithmic Differentiation   HW p.170/19,20,43-46; p.172/22
           3.6 Parametrics  CW p.147-148/50-58, 66, 68, 71

10/19  Review
10/20  Test of Chapter 3  Post-Test HW read 4.1, do p.184/1-25 odd

Post test homework - intro to the Chain Rule

You homework is to take a peak at the Chain Rule - the last of our derivative rules. Read section 3.6 and do p.146-147/1-27 odd.  I will prove it tomorrow.

Questions from today's handout

You may have already noticed but at the top of today's handout of problems it mentions that you can get worked solutions for the odd problems from www.CalcChat.com (though you may need to download Shockwave to use it).

I noticed also that problem 6 is really a Chain Rule problem (sneaky cx) so you can skip that one.

Here are my answers for the even problems:
2.  y - 4 = 4(x - 2)  and  y - 1 = -2(x + 1)
4.  a] tangent  y - 4 = 4(x - 2)
    b] normal   y - 4 = =0.25(x - 2)
    c]  y = 0
    d]  normal = curve:  y = (-1/2a)(x - a) + b = x^2 (where b = a^2)
         if you use the quadratic formula to solve for x you find the
          discriminant is positive so there are two solutions.
6.  skip it
14.a]  v = (-27/5)t + 27  and  a = -27/5
    b]  v = 27(1 - .2t) = 0  so  t = 5
    c]  a = 5.4 ft/sec^2 rather than 32 ft/sec^2, about 1/6^th