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• FETMaths

This module and collection are included inLens: Siyavula: Mathematics (Gr. 10-12)
By: Siyavula

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# Summary and exercises

## Average Gradient: Summary and exercises

• The average gradient between two points is: y 2 - y 1 x 2 - x 1 y 2 - y 1 x 2 - x 1
• The average gradient of a straight-line function is the same over any two intervals on the function
• The average gradient of a parabolic function depends on the interval and is the gradient of a straight line that passes through the points on the interval
• We can extend the concept of average gradient to any function

## End of Chapter Exercises

1. An object moves according to the function d=2t2+1d=2t2+1 , where dd is the distance in metres and tt the time in seconds. Calculate the average speed of the object between 2 and 3 seconds. The speed is the gradient of the function dd
2. Given: f(x)=x3-6xf(x)=x3-6x. Determine the average gradient between the points where x=1x=1 and x=4x=4.
3. Find the average gradient of each of the following functions between the points where x=2x=2 and x=3x=3
1. f(x)=x2+3f(x)=x2+3
2. f(x)=4x+1f(x)=4x+1
3. f(x)=2x-3f(x)=2x-3

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#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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##### Lenses

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##### What is in a lens?

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