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    By: Siyavula

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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
    Click here for the solution
  2. Given: f(x)=x3-6xf(x)=x3-6x. Determine the average gradient between the points where x=1x=1 and x=4x=4.
    Click here for the solution
  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
    Click here for the solution

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