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

Estimate the rate of change of the graphed function over the interval -4 <_ x &lt-example-1
User Tim Pesce
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1 Answer

4 votes

Answer:

0.2071

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."

Estimate the rate of change of the graphed function over the interval -4 <_ x &lt-example-1
User Alium Britt
by
7.7k points
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