Week 5 of m171
(§ 3, Mr. Lane)
20–24 February 2017
Math Learning Center (in Math 011) has tutors:
10am–4pm on Monday–Thursday and
10am–1pm on Friday
math@Mansfield (Library) has tutors:
6:30pm – 9:00pm on Sunday–Thursday
- Monday (20 February 2017) —
Presidents' Day (third Monday in February),
no classes at U MT
- Tuesday [d15]
WeBWorK:
RQ-3-1 closes at noon,
day-13 closes at 11 pm
- Use limit definition of derivative to examine these claims.
Suppose p(x) = x · g(x)
where g is a differentiable function. Then
- p is a differentiable function
- p'(x) =
g(x) + x · g'(x)
- That derivative formula
has a geometric interpretation.
- Study section 3.1 (Powers and Polynomials).
- The Power Rule (page 126) reports the derivative of x^{n}.
Our text uses the Binomial Theorem (on page 127) to justify
that formula for the case when n is a positive integer.
An alternative justification can use today's item (1).
- The derivative of a constant multiple and of a sum (or difference)
involves easy algebra.
- A polynomial is the sum of constants multiplying
non-negative integer powers
- Work on these items at end of §3.1:
3–5, 13, 20, 34, 41;
50–55, 58, 61, 69, 75;
83, 84, 89, 90
- Wednesday [d16]
WeBWorK:
RQ-3-2 closes at noon,
day-14 closes Thursday at 11 pm
- Study section 3.2 (The Exponential Function).
- We already know
rate-of-change for a linear functions is constant.
- Relative rate-of-change for an exponential function
is constant.
If g is an exponential function, then
g′ / g is constant.
- Work on these items at end of §3.2:
1, 5, 13, 17, 21;
31 & 32, 39, 43, 45;
49–53
- Anticipate a quiz.
- Friday [d17]
WeBWorK:
RQ-3-3 closes at noon,
day-15 closes Saturday at 11 pm
- Write-up solutions of these four problems —
show your work and interpret your results. Hand-in your written
homework at the start of Friday's class.
section |
2.5 |
2.6 |
3.1 |
3.2 |
problems |
26 |
16 |
74 |
40 |
- Use limit definition of derivative to examine these claims.
Suppose p(x) = g(x)^{2}
where g is a differentiable function. Then
- p is a differentiable function
- p'(x) =
2 · g(x) · g'(x)
- That derivative formula
has a geometric interpretation.
- Study section 3.3 (Product and Quotient Rules).
- Apply today's item (2) to g(x) = A(x) + B(x).
After some algebra, we can discover the Product Rule:
(A · B)′
= A′ · B + A · B′
- Figure 3.13 (page 137) is a good illustration of
the Product Rule.
- A special case of the Quotient Rule is easy to prove:
derivative of 1 / g(x)
equals − g′(x) / g(x)^{2}
- Work on these items at end of §3.3:
1, 3, 9, 13, 19, 27;
31, 33, 34, 41, 43, 55;
66–68, 71
© Richard B Lane
Last modified: 17 February 2017, Friday 09:14