Category: 12 SL Homework

Complete the following questions before our next class.

Exercise 18D questions 2, 3, 11, 12
Exercise 18E.1 questions 1cdg, 2cd, 3de, 5ab
Exercise 18E.2 questions 1bc, 2b, 3ac

Complete the following questions before our next lesson.

Exercise 17C questions 1, 2, 6, 8, 11, 14, 19

Complete the questions below before our next class.

Exercise 17A.1 question 2
Exercise 17A.2 questions 1, 2, 4, 6
Exercise 17B questions 1, 2, 5, 8, 9, 10, 13

Complete the following for our next lesson.

Exercise 16D.1 questions 2cf, 3efh, 9
Exercise 16D.2 questions 1, 2
Review Set 16C question 13

In class we defined a stationary point, and noted that a stationary point may be a local maximum or a local minimum. There is, however, a third option, as illustrated by the function \(f(x)=x^3\) when \(x=0\). While the function does have a stationary point at \(x=0\), it is neither a local maximum, nor a local minimum, instead, it’s called a point of inflection.

Read Section 16C, then try questions 1 and 2ac in Exercise 16C before our class on Wednesday.

After today’s review of techniques for differentiation, try the questions listed below before our next class.

We’ve already seen how to find the equation of the tangent line to a curve that passes through a given point, and finding a normal through a given point on a curve is essentially the same. A normal is a line that is perpendicular to a tangent, and you will recall that if one line has slope \(m\), any line perpendicular to it will have slope \(-\frac{1}{m}\). For example, the equation of the line tangent to the function \(f(x)=x^2\) that passes through the point \((1,1)\) has slope \(2\) (found by taking the derivative), and so has equation \(y=2x-1\). Similarly, the normal to the function \(f(x)=x^2\) that passes through the point \((1,1)\) has equation \(y=-\frac{1}{2}x-1\).

We’ve now covered the derivatives of logarithmic and trigonometric functions, and the questions below involve applications of those derivative results.

For logarithmic functions, you may find it easier to simplify some expressions using the properties of logarithms before you try to differentiate. See the list of properties of logarithms at the bottom of page 376, and you can see an example of how these can simplify your calculations in Example 12 on page 377.

Exercise 15F 1ghk, 2adeh, 3abegi, 5
Exercise 15G 1adgh (see page 379 for more about the derivative of \(\tan x\), 2adgk, 3bek, 4b

Complete the following questions before our next lesson.

Exercise 15D (the quotient rule) questions 1abf, 2ad, and 4.
Exercise 15E (the derivative of the exponential function) questions 1ijno, 2acg, 3a, and 5.

Complete the following questions for our next class.

Exercise 15B.2 questions 1ad, 2abcdfi, 3acef, 4, 5

Have a look at the questions in the section below prior to tomorrow’s class, and we’ll be working on these during part of tomorrow’s class.

Exercise 15A questions 1aejno, 2ab, 3bf, 4abc, 5, 7.