Communication (12 marks) 2. a) Consider the function y = sinx. State the following derivatives: (3 marks) i) y' = ii) y" = iii) y" = (3'd derivative) b) Use the patterns from above to determine y(99) , 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 Ify = et (x), then y' = ef'(x) g)Thinking (11 marks) 4. Show, using the derivatives of primary trig functions, that dx csc(x) = - csc(x) cot(x) 5 . Find the equation of the tangent to y = at X = T. cos(x)Application (12 marks) 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0 S x 5 2x S b) Classify each critical value as a minimum, maximum, or stationary point. (Explain your answer) NI7. Cindy and her friends start a rumour about Matt and write it on Facebook. The rumour quickly spreads among the students at nts at school. After t days, the number of students who have heard the rumour is given by n(t) 700 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? c) Determine n'(5) . Explain the meaning of the result. 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 - 400 - 300 200 - 100 - # Days