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

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

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

y=1/4x-4

step-by-step explanation: