Question: Consider the function f(x) = x 3 + 1 Determine the average rate of change between the points x 1 = -1 and x 2

  1. Consider the function f(x) = x3 + 1 Determine the average rate of change between the points x1 = -1 and x2 = 3
  2. Consider the functionf(x) = -x2 + 4x + 21 Determine the average rate of change between the points x1 = 4 and x2 = 10

  1. Consider the function f(x) = 3x3 - 7 Using the difference quotient for tangent lines, determine the instantaneous rate of change at the pointx = 1 by choosing the following values for h: a) h = 1 b) h = 0.1 c) h = 0.01
  2. Comment on your results in parts a to c above. Which value of h gives you the best estimate of the instantaneous rate of change at the point x = -1? Why? What can you do to get an even better estimate of the instantaneous rate of change at the point x = -1.

Find the value of the instantaneous rate of change for each of the following functions at the specified x-value a) f(x) = x3 - 2x2 - 3 at x = 2 b) f(x) = x2 + 2x + 14 at x = -5

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