Question

is average rate of change of the function, g(x)=x^2, over interval [-1,1] equal to 0?

Answer 1

the average rate of change over any interval [a,b] is just:

f(b) - f(a)
--------
b-a

Answer 2

in your case:
\[\frac{g(1)-g(-1)}{1-(-1)}\]

Answer 3

\[\frac{(1)^2-(-1)^2}{1-(-1)}=\frac{1-1}{1+1}=\frac{0}{2}=0\]

Answer 4

and yes, the average rate of change over a parabola between 2 points that are the same height is 0 :)

Answer 5

Thank you!