Posted by Shaila on Sunday, September 26, 2010 at 3:02am.
a) Describe a graph for which the average rate of change is equal to instantaneous rate of change for its entire domain. Describe a real life situation that this graph could represent.
b) Describe a graph which the average rate of change between two points is equal to the instantaneous rate of change at:
i) one of the two points
ii) the midpoint between two points
c) Describe a real life situation that could be represented by each of the graphs in part b)

Math  Instantaneous and average rates of change  MathMate, Sunday, September 26, 2010 at 2:43pm
a)
The equivalent statement is that:
since the instantaneous rate of change is equal to the average rate of change throughout the domain, the instantaneous rate of change does not vary.
How would you describe a function for which the instantaneous rate of change does not vary?
b)
The midpoint theorem in mathematics says that the average rate of change of a function between two points is equal to the instantaneous rate of change of at least one point between the two endpoints. Therefore the graph of any curve would satisfy condition (b)(i).
For part b)(ii), you need to draw a graph in which the tangent to the curve at the midpoint is equal the chord joining the two endpoints.