Correct option is:
Choice C.
Explanation:
We have the following quadratic function:
[tex]f(x)=x^2-x-1[/tex]
We know that at the vertex of a quadratic function we'll have either a maximum or minimum in whose case the Average Rate of Change will be zero.
For any quadratic function the vertex is:
[tex]Vertex:(h,k) \\ \\ \\ h=-\frac{b}{2a} \\ \\ \\ Here: \\ \\ a=1 \\ \\ b=-1 \\ \\ c=-1 \\ \\ \\ x=-\frac{-1}{2(1)} \\ \\ h=\frac{1}{2}=0.5 \\ \\ \\ k=f(-\frac{b}{2a}) \\ \\ k=f(\frac{1}{2})=(0.5)^2-(0.5)-1 \\ \\ k=-\frac{5}{4}=-1.25[/tex]
So at [tex]x=h=0.5[/tex] the function will have an average rate of change of zero. Both Choice C and D meet the requirement because [tex]x=h=0.5[/tex] lies on these intervals , but we'll just choose Choice C since this is the least interval. So:
Correct option is:
Choice C.
Learn more:
Derivative: https://brainly.com/question/13419010
#LearnWithBrainly
