To find the average rate of change for a function over a specific interval, we need to calculate the difference in the function values at the two endpoints of the interval and divide it by the difference in the corresponding x-values.
The function f(x)=-x^2+x-5.
At the right endpoint x=1, f(1)=-(1)^2+1-5=-5.
At the left endpoint x=-5, f(-5)=-(5)^2+5-5=-25.
The difference in the function values is f(1)-f(-5)=-5-(-25)=20.
The difference in the x-values is 1-(-5)=6.
Therefore, the average rate of change of the function over the interval -5<x<1 is 20/6, which simplifies to 10/3.
What is the average rate of change for the function f(x)=-x^2+x-5 over the interval -5\<x\<1?
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1 answer