Find the average rate of change of g(x)=-x^2+2x+2 from x=2 to x=6

Question

jhonyy9 · Answer

for x=2 you get 10

for x=6 ---- 50 

what is the average rate ?

anonymous · Answer

just consider the end points, it doesn't matter what the function does in between. g(6)-g(2)/(6-2)

anonymous · Answer

would it be 4?

whpalmer4 · Answer

average rate of change of a function $f(x)$ between the points $(a,f(a))$ and $(b,f(b))$ is simply the slope of a line through those two points, and therefore is $$\frac{f(b)-f(a)}{b-a}$$

whpalmer4 · Answer

what is $g(6)=$
what is $g(2)=$

anonymous · Answer

g(6)= -22 and g(2)= 2

whpalmer4 · Answer

okay, what is $$\frac{g(6)-g(2)}{6-2}=$$

anonymous · Answer

-24/4 ?

whpalmer4 · Answer

Here's a graph showing both the curve (in blue) and the line passing through those two points.

whpalmer4 · Answer

yes, slope is $-24/4 = -6$

anonymous · Answer

So -6 is the average rate of change?

whpalmer4 · Answer

yes.  the average rate of change is just the slope of the line that goes through the endpoints of the region of interest.  matters not a whit what the function does in between them.