Find the average rate of change on the interval [-6,3] of the function h(x)=x^2-4x+7.
A. -7
B. 7
C. 1
D. 13
E. -5
h(-6)=36+24+7
h(3)=9-12+7
h(3)-h(-6)=27+36=63
rate of change= 63/(3-(-6))=7
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To find the average rate of change on the interval [-6,3] of the function h(x) = x^2 - 4x + 7, we need to calculate the slope of the line connecting the values at the endpoints.
First, let's find h(-6) and h(3):
h(-6) = (-6)^2 - 4(-6) + 7
= 36 + 24 + 7
= 67
h(3) = (3)^2 - 4(3) + 7
= 9 - 12 + 7
= 4
Now, we can find the average rate of change:
Average rate of change = (h(3) - h(-6)) / (3 - (-6))
= (4 - 67) / (3 + 6)
= (-63) / 9
= -7
Therefore, the average rate of change on the interval [-6,3] is -7. The correct answer is A. -7.
To find the average rate of change of the function h(x) over the interval [-6, 3], we need to evaluate the function at the endpoints and calculate the difference in the function values divided by the difference in the x-values.
The average rate of change (AROC) formula is given by:
AROC = (h(b) - h(a)) / (b - a),
where "a" and "b" represent the endpoints of the interval, and "h(a)" and "h(b)" represent the function values at a and b, respectively.
For the given function h(x) = x^2 - 4x + 7, we can find the function values at the endpoints:
h(-6) = (-6)^2 - 4(-6) + 7 = 36 + 24 + 7 = 67,
h(3) = (3)^2 - 4(3) + 7 = 9 - 12 + 7 = 4.
Substituting these values into the AROC formula:
AROC = (h(3) - h(-6)) / (3 - (-6))
= (4 - 67) / (3 + 6)
= (-63) / 9
= -7.
Therefore, the average rate of change of the function h(x) over the interval [-6, 3] is -7.
So, the answer is A. -7.