Question

Estimate the rate of change of the graphed function over the interval -4 <_ x <_ 0

Answer 1

Answer:

  0.2071

Step-by-step explanation:

It looks like the graph is of the function ...

  y = √(x +8) -2

We know that (-4, 0) is one point on the graph. The other point of interest is at x=0, where y = √8 -2 ≈ 0.8284.

The average rate of change on the interval is then ...

  m = (0.8284 -0)/(0 -(-4)) = 0.2071

The average rate of change on the interval is about 0.2071.

_____

Rougher estimate

The graph goes through the points (-4, 0) and (1, 1), so has a slope of 1/5 = 0.2 on the interval [-4, 1]. We know the graph does not go through (0, 1), so the slope is not as high as 1/4 = 0.25. The curve is concave downward, so the average slope will be higher than 0.2, but we aren't sure how much higher.

A reasonable estimate of the rate of change on the interval is "a little more than 0.2, but less than 0.25."