Question

What is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4

Answer 1

Answer:

  2

Step-by-step explanation:

For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.

The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...

  f'(1) = 2(1) = 2

The average rate of change of f(x) on [-2, 4] is 2.

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Alternate solution

The average rate of change is the slope of the line between the end points of the interval:

  m = (y2 -y1)/(x2 -x1)

  m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2

The average rate of change on [-2, 4] is 2.

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The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.