Answered

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Given the function h(x)=-x^2+x+4, determine the average rate of change of the function over the interval −1≤x≤5.

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Answer:

average rate of change of h(x) on −1 ≤ x ≤ 5 is then 5

Step-by-step explanation:

   

                                            change in h(x)

average rate of change = ------------------------

                                            change in x

Calculate h(x) at the interval endpoints:  -1 ≤ x ≤ 5, and then subtract h(5) from h(-1):

h(5) = (5)² + 5 + 4 = 34

h(-1) = (-1)² -1 + 4 = 4

change in h(x) = 34 - 4 = 30

change in x:  5 - (-1) = 6                                                 30

average rate of change of h(x) on −1≤x≤5 is then  ------------- = 5

                                                                                         6

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