Math 006 - Handout for Week 12

The exam will be

Suggested exercises to try from text book for preparing for exam:
2.1: 2, 13.	2.2: 3, 4, 7.	2.6: 1, 7, 8.	3.5: 3.	4.2: 4.	5.5: 3 - 8.	7.2: 1.	8.2: 4.	8.4: 1.

Exam type questions:

1. Where has the tangent to x3 - 5x got slope 4? Find the equations for the tangents at these points. 2. Find the derivatives of the following functions: a. (x3 + 9x2 + 7)/(3x2 - 9) b. (x3 + x2 + x + 1)10 (2x3 + 3x2 + 5)11 c. ln(cos(ex)) d. e(x2 + x sin(x2 + 1)) e. (x3 + 3)(-1/3) f. 8x + 7x 3. Sketch the graph of the derivative of the function sketched below. 4. Find the absolute maximum and minimum of the function f(x) = x5 - 2x3 + x + 1 on the interval [0,2] 5. If the width of a square increases at 5m/s, and the length increases at 3m/s what is the rate of increase in the area when the width is 4m long, and the length 7m long? 6. Find the intercepts, asymptotes, domain, local max and min, intervals where increasing, decreasing, concave up, concave down, of the function f(x) = (x3 + 1)/(x2 - 4). Use this information to sketch a graph of this function.

You will be able to find the answers at http://www.mast.queensu.ca/~helena/math006/sampleexam.html

What will be on the exam (1) Chapter 2; 7.2; 8.2; 8.4: Find the derivative of list of functions, including functions involving sine, cosine, exponential and logarithmic functions, in combination with polynomials. (2) Chapter 2: Find the equations for tangents of graphs, and tangents with given slope. (3) 5.5: Long detailed question to sketch a curve, including finding concave up, concave down, like assignment 8 examples. (4) 2.1: Given a sketch of a graph, sketch the derivative (like homework: page 75, 2.1, Ex 2, page 77 Ex 13) (5) 3.5: Related rates problem. (6) 4.2: Problem about finding absolute max and min on an interval.

Note: You will not be expected to simplify expressions after taking the derivative. You will not have to learn anything about limits for the exam. You will not have to learn anything not included in the above sections of the text or on the above web pages. Remember to bring a calculator to the exam.
I will be away for Monday Tuesday next week, so please come and ask any questions before then. (My office is 401 Jeffrey, email helena@mast.queensu.ca ). There will still be a tutorial with the TA on Tuesday, 2.30 - 3.30pm, in room 116.