16.6k views
0 votes
Given the function h(x)=-x^2+x+4, determine the average rate of change of the function over the interval −6≤x≤4.

User Stine
by
8.0k points

1 Answer

7 votes
The average rate of change of a function over an interval is given by the formula:

Average rate of change = (f(b) - f(a)) / (b - a)

where a and b are the endpoints of the interval.

In this case, the interval is −6≤x≤4, so a = -6 and b = 4. The function is h(x)=-x^2+x+4, so:

h(-6) = -(-6)^2 + (-6) + 4 = -20
h(4) = -(4)^2 + (4) + 4 = -8

Therefore, the average rate of change of h(x) over the interval −6≤x≤4 is:

Average rate of change = (h(4) - h(-6)) / (4 - (-6))
= (-8 - (-20)) / (4 + 6)
= 12 / 10
= 1.2

So the average rate of change of the function over this interval is 1.2.
User Modesitt
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories