Answer:
Step-by-step explanation:
The average rate of change is an algebra thing, whereas the instantaneous rate of change is a calculus thing. Since this is not a straight line we are simply finding the slope of the straight line that connects the 2 coordinates (4, y) and (9, y). To find the y's in each case, sub in the x value and solve for y:
If [tex]y=\sqrt{x+6}[/tex] when x = 4, then [tex]y=\sqrt{10}[/tex] and the coordinate is [tex](4,\sqrt{10})[/tex].
Likewise for the other coordinate when x = 9. [tex]y = \sqrt{15}[/tex] and the coordinate is [tex](9,\sqrt{15})[/tex]
Using the slope formula,
[tex]m=\frac{\sqrt{15}-\sqrt{10} }{9-4}[/tex] and
[tex]m=\frac{\sqrt{15}-\sqrt{10} }{5}[/tex] and
m = .14 rounded
