Calculus for Phys./Life Sciences 1

Exam #3

Wednesday, Nov. 30, 6:00 - 7:30 pm

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, 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: Both sections will 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.)