Tuesday Oct 17
Solve, write up and turn in: Sec. 4.1- 18, 22, 23, 24, 25, 27, 29
Problems 18, 22 need (for easier solutions) the use of intervals of increase/decrease or the second derivative test. Solve them after we discuss these issues.
FYI - solving polynomials-web resources: Here is how The cubic formula looks like. This web article is very nice, please read it.
after reading the article above you are still curious about the
formula for solving polynomials of fourth degree,
you can check this website: Solving Quartic Equation
polynomials degree 5 and higher there are no general formulas for
roots which involve radicals only.
Wednesday Oct 18
Topics: A.3, 4.1
Solve, write up and turn in: Sec. 4.1- Now it is a good time to solve 18, 22 (see below also)
1. In problem 18 it is easy to find the zeroes of the derivative.
The derivative does not change the sign between its zeroes. Explain why!
2. Find the intervals of increase, decrease, local maxima, minima and graph the function
y=x(x-1)^(1/3) Caution: you have a radical, therefore there is a point where the derivative does not exist.
Show on the graph what happens there.
Sec. 4.1: 7, 9, 11, 13, 30
Topics: 3.6, 4.2,
Web resource: Referring angles to an acute one(preferred)
and another one: Trig functions for any angle
see also Sec. 1.7
Solve: Sec. 1.7 3, 7
Find the period of sin(3x+4), and of tan(5x).
<>Solve, write up and turn in:
Sec. 4.2 1, 7, 9, 10, 15, 18, 21, 27
Sec. 3.6 3a, 5
3. Show that if a function is concave up, then
the graph is above its
Hint: the y on the graph is y=f(x). The y on the tangent at (x0,y0=f(x0)) is y=f(x0)+f'(x0)(x-x0).
So you need to show that f(x)>f(x0)+f'(x0)(x-x0) for all x.
Define the function g(x)=f(x)-f(x0)-f'(x0)(x-x0) and show that this function g(x) has a minimum at x=x0.
(How? Use the derivative g'(x), of course.)
Midterm exams are during
the regular class hour and room.
Review guide for Exam 1
Topics: 2.4 velocity, acceleration, 4.3
Read Example 3 Sec. 4.3
Solve, write-up and turn in:
Sec. 2.4: 9
Sec. 4.3: 1, 3, 5, 11, 28, 31
Information for Exam 1:
Review guide for Exam 1
A few review problems:
Use the epsilon-delta definition of the limit to show that the limit of (3x-1), as x goes to 1, is 2.
Additional problems for Chapter 2 (Page 81):
Use the definition of the derivative in 6a,b.
Where is the function continuous, where is it differentiable: 7b.
19, 25, 29, 41
Additional problems for Chapter 3 (Page 111):
1, 5, 7, 33b,g,o, 38, 40 a
The Homework problems in Chapter 4.
Show that if f(x) is continuous on [0,5] and f(0)=3, f(5)=4, then there is a c between 0 and 5 so that f(c)=pi.