Complete the following questions before our next class.
Exercise 18C questions 3bcd, 4
Exercise 18H (here you can use the results we derived in class) questions 1dfg, 2ahj, 3a
11 SL Vectors
Complete as many of the following questions as you can before our next class.
Exercise 12A.2 questions 2 and 3
Exercise 12B.1 questions 2 and 3
Exercise 12B.2 questions 1a and 3
Exercise 12B.3 questions 1df and 2
Exercise 12B.4 questions 1abce, 2, 3–5
11 HL The Chain Rule
Complete the following questions before our next class.
Exercise 18B.2 questions 2fhi, 3aef, 4, 5
11 HL Derivatives of Functions
Complete the following questions before our next lesson.
Exercise 18A questions 1dhlno, 2bce, 3bfg, 4bd, 5
11 HL Working with Derivatives
Following on from our discussion from class, complete the following question.
Let \(f(x)=\frac{1}{3}x^3-2x^2\). Find the coordinates of the local maximum and the local minimum of \(f\).
Are you interested in seeing something else that’s sort of neat? Read on.
We’ll eventually be discussing something called the second derivative. Once you’ve found the derivative of a given function, you can then go on to find the derivative of that derivative. For example, if \(f(x)=2x^5\), then \(f'(x)=10x^4\). The second derivative is represented as \(f^{\prime \prime}(x)\); in this case, we have \(f^{\prime \prime}(x)=40x^3\).
Find the second derivative of the function \(f(x)=\frac{1}{3}x^3-2x^2\), then solve the equation \(f^{\prime \prime}(x)=0\). On the graph of \(f\), plot the point on \(f\) whose \(x\)-coordinate is the solution you found to \(f^{\prime \prime}(x)=0\). What do you notice about the location of this point?
11 SL Double-Angle Formulas
Complete the questions below (which will be good preparation for our test on Friday).
Exercise 11D questions 7gjm, 8a, 9a, 10b
Exercise 11E 1de, 2ade
11 SL Trigonometric Identities and Expressions
In order to make use of the trigonometric identities we discussed today, it is frequently also necessary to be able to simplify or factor expressions involving trigonometric functions.
The questions below give you some opportunity to practice simplifying and factoring, then you’ll use those skills when applying the double-angle formulae. Complete these questions before our next class (and these may be checked on Monday…).
Exercise 11C.1 questions 1aef, 2d, 3acd, 4ad
Exercise 11C.2 questions 1ace, 2af, 3af
Exercise 11D questions 1–5
11 HL Limits
Complete the following before our next class.
Exercise 17A questions 1, 2c, 3, 5ai
Exercise 17B.1 question 2
Exercise 17B.2 question 1
11 SL Trigonometric Equations and Models
Now that we’ve covered some techniques for solving trigonometric equations, we can make use of those techniques in situations involving trigonometric models. Complete the questions below before our next class.
Exercise 11B questions 3, 5, and 6
11 SL Solving Trigonometric Equations
Try your best to complete the following questions for our next class. (Some of these will be more difficult than what we considered in class, so do your best to find answers on your own and we’ll look at the more difficult questions on Monday.)
Exercise 11A.2 questions 2ab, 4
Exercise 11A.3 questions 1, 2, 5, 6efg, 7