Communication (12 marks) 2. a) Consider the function y = sinx. State the following derivatives: (3 marks) i ) y' = ii) y" = iii) y" = (3rd derivative) b) Use the patterns from above to determine y), the 99th derivative. (Explain your answer) (2 marks) 3. True/False Statements: Indicate whether the statement is true or false. (7 marks) a) The derivative of a sinusoidal function is another sinusoidal function. b ) A sinusoidal function can be differentiated only if the independent variable is measured in radians. C) There is an infinite number of tangents with a given non-zero slope to a sinusoidal curve. d) The rate of change to a sinusoidal function is periodic in nature. e) Another way of expressing In x is loge x f) The nth derivative of y = ex will always be ex g) Ify = ef (x), then y' = ef'(x)7. Cindy and her friends start a rumour about Matt and write it on Facebook. The rumour quickly spreads among the students at school. After t days, the number of 700 students who have heard the rumour is given by n(t) =- 1+34e- . a) What is the initial number of people who started the rumour? -1 b) How many people know about the rumour after 3 days? -41 c) Determine n'(5) . Explain the meaning of the result. WI d) Graph the function over the first 10 days is shown. After how many days is the rumour spreading the fastest? Why might the rate of change slow down after this point? 700 600 - 500+ NI # People 400 300 + 200 + 100 + + + # Days