Thursday

July 24, 2014

July 24, 2014

Posted by **Shaila** on Sunday, September 26, 2010 at 3:02am.

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 2:43pma)

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 mid-point 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 end-points. 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 mid-point is equal the chord joining the two end-points.

**Related Questions**

Math - Rates os change - a) Describe a graph for which the average rate of ...

MATH - Create a graph of a function given the following information: The ...

Math - Could someone help me with these questions, I don't know question c) and ...

Math~Reinyyy - Could someone help me with these questions, I don't know ...

instantaneous rate of change problem - Joe is investigating the rate of change ...

calculus - i'm not sure how to do this. can someone help, please? thanks! ...

Instantaneous rate of change - Please help.. Joe is investigating the rate of ...

Calulus - Consider the following function. f(t) = 3t2 − 3 (a) Find the ...

rate of change - Joe is investigating the rate of change of the function y=cos x...

function rate of change - Joe is investigating the rate of change of the ...