Calculus for Phys./Life Sciences 1
Exam #3
Wednesday, Nov. 30,
HABERLIN 103 (in the basement)
The third exam covers Sections 3.5 - 3.10 of
Chapter 3 and Sections 4.1, 4.3, 4.5 - 4.7 of Chapter 4. The exam will be
designed to take an hour but you will have an extra 30 minutes to check your
work.
In Chapter 3, topics include derivatives of
trig functions, implicit differentiation, logarithmic differentiation (similar
to Problem A in Assignment 7), derivatives of inverse functions, tangent line
approximations, hyperbolic functions, the Mean Value Theorem and other theorems
about differentiable functions. In Chapter 4, topics include finding extrema
(local maxima and minima), critical points, the first and second derivative
tests for classifying critical points, concavity, inflection points, global
max's and min's, optimization problems, related rates and L'Hopital's Rule.
Note that you still need to know all the differentiation rules (ie. the power,
product, quotient and chain rules, etc.) in order to calculate derivatives.
It is recommended that you go over homework
problems as well as your class notes. Many of the problems and questions we
discuss in class are excellent examples of test questions. I have also listed
some sample problems from the Chapter 3 and 4 Reviews as well as the Chapter 3
and 4 Check Your Understanding Sections below. Answers to the even numbered
problems are provided. Click here for a Practice
Exam (PDF file). Note that question #1 on parametric equations is NOT
covered on this exam. Solutions (PDF
file) are available here. It is recommended you try the exam first before
looking at the solutions.
Note: You will be given a scientific calculator for the exam which does NOT
have graphing capabilities so be prepared to answer questions without your
personal calculator.
Exam Review: We will have a review for the exam during Tuesday's
class, Nov. 29th. Please come prepared with specific questions.
Review Problems: The answers to the odd problems are in the back of the
book. The answers to some of the evens are provided.
Chapter 3 review, pp. 159 - 162
Problems: 3, 7, 11, 15, 25, 27, 29, 45, 55, 63, 67, 69, 71, 79, 84e,
84f, 91, 93
Even Solutions:
84e. f'(2) = sin(3) - 8 cos(3)
84f. f'(2) = 4 ln 3 - 16/3
Chapter 3 Check Your Understanding, pp.
163 - 164
Problems: 5, 9, 11, 14, 15, 18, 32, 33
Even Solutions:
14. False; sinh^2 x is concave up everywhere
18. False; try f(x) = e^x
32. False, f(x) = |x| is an example
Chapter 4 review, pp. 229 - 233
Problems: 1, 3, 5, 9, 12, 15, 17, 25, 26, 27, 30, 31, 35, 37, 40, 48,
49, 51, 54, 55, 57, 58
Even Solutions:
12. Global Max is 1/2 at x = 1.
26. (a) x_3, (b) x_1 and x_5, (c) x_2, (d) 0
30. (a) Decreasing for x < -1 and 0 < x < 1, increasing for -1
< x < 0 and for x >1.
30. (b) Local mins at x = -1 and x = 1. Local max at x = 0.
40. (a) C(x) = 2 sqrt(x^2 + 300^2) + 1000 - x, (b) 173.21 miles.
48. -25/2
54. -0.0545 m^3/min
58. (a) volume decreases, (b) -0.25 cm^3/min
Chapter 4 Check Your Understanding, pp.
234 - 235
Problems: 3, 5, 7, 13, 16, 17, 21, 22
Even Solutions:
16. True, dc/dt = 2 Pi dr/dt
22. Impossible (try drawing such a function.)