Unit 1: Rates of Change Assessment Opportunity Instructions There are 10 questions in this Assessment Opportunity for a total of 60 marks. Show all work for each question.

1. Determine the average rate of change of y in the function y= 2 x 3+ 7 x 2+ 2x 3 over the interval [3,5]. (5 marks)

2. Given the function f(x)= 2 x 2+ 3x+ 1,

a. Use the secant method to find the instantaneous rate of change when x= 1.

b. Use First Principles to find the value of the derivative when x= 1.

c. What did you notice?

3. Explain the difference between a secant line and a tangent line. How do they relate to the rate of change of a function? Include a sketch of each type of line in your solution.