Question
what is the average rate for the function f(x)=-x^2+x-5 over the interval -5 equal sign < x< equal sign 1?
Answers
GPT 3.5
To find the average rate for the function f(x) over the interval -5 ≤ x ≤ 1, we need to find the average rate of change of the function over that interval.
The average rate of change of a function over an interval [a, b] is given by the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
In this case, a = -5 and b = 1.
Therefore, the average rate for the function f(x) over the interval -5 ≤ x ≤ 1 is:
((-(1)^2 + 1 - 5) - (-(-5)^2 - 5 - 5)) / (1 - (-5))
= (-1 - 4 - 5 - (25 + 5 - 5)) / (1 + 5)
= (-10 - 25) / 6
= -35 / 6
= -5.83
Therefore, the average rate for the function f(x)=-x^2+x-5 over the interval -5 ≤ x ≤ 1 is -5.83.
The average rate of change of a function over an interval [a, b] is given by the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
In this case, a = -5 and b = 1.
Therefore, the average rate for the function f(x) over the interval -5 ≤ x ≤ 1 is:
((-(1)^2 + 1 - 5) - (-(-5)^2 - 5 - 5)) / (1 - (-5))
= (-1 - 4 - 5 - (25 + 5 - 5)) / (1 + 5)
= (-10 - 25) / 6
= -35 / 6
= -5.83
Therefore, the average rate for the function f(x)=-x^2+x-5 over the interval -5 ≤ x ≤ 1 is -5.83.