Question: Given the function f ( x )= 2 x 2+ 3 x + 1 1a. Find the instantaneous rate of change when x = 1.

Given the functionf(x)= 2x2+ 3x+ 1

1a. Find the instantaneous rate of change whenx= 1.

1b. Find the value of the derivative whenx= 1.

1c. What did you notice?

2.The path of a baseball relative to the ground can be modelled by the functiond(t)= t2+ 8t+ 1, whered(t)represents the height of the ball in metres, andtrepresents time in seconds.

2a. Find the average rate of change of the ball between 1 and 3 seconds.

2b.Using the secant method, find the instantaneous rate of change at 2 seconds.

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.

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