Question

Find the average rate of change of f(x) sq rt x+6 = on [4, 9]. Round your answer to the nearest hundredth.

Answer 1

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 $y=\sqrt{x+6}$  when x = 4, then $y=\sqrt{10}$  and the coordinate is $(4,\sqrt{10})$.

Likewise for the other coordinate when x = 9.  $y = \sqrt{15}$ and the coordinate is $(9,\sqrt{15})$

Using the slope formula,

$m=\frac{\sqrt{15}-\sqrt{10} }{9-4}$ and

$m=\frac{\sqrt{15}-\sqrt{10} }{5}$ and

m = .14 rounded