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Average gradient: summary and exercises

  • The average gradient between two points is: 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 = 2 t 2 + 1 , where d is the distance in metres and t the time in seconds. Calculate the average speed of the object between 2 and 3 seconds. The speed is the gradient of the function d
  2. Given: f ( x ) = x 3 - 6 x . Determine the average gradient between the points where x = 1 and x = 4 .
  3. Find the average gradient of each of the following functions between the points where x = 2 and x = 3
    1. f ( x ) = x 2 + 3
    2. f ( x ) = 4 x + 1
    3. f ( x ) = 2 x - 3

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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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