Question

Use the image to answer the question.

A curve labeled m of x and seven points on the curve are plotted on a coordinate plane. The curve begins on the x-axis sloping upward from left to right, passes through quadrant 2, and then rises through quadrant 1.
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The values on the x-axis range from negative 4 to 10 in increments of 1. The values on the y-axis range from negative 2 to 4 in increments of 1. The curve passes through the following plotted points: left parenthesis negative 2 comma 0 right parenthesis, left parenthesis negative 1 comma 1 right parenthesis, left parenthesis 2 comma 2 right parenthesis, left parenthesis 3 comma 2.2 right parenthesis, left parenthesis 4 comma 2.4 right parenthesis, left parenthesis 7 comma 3 right parenthesis, and left parenthesis 10 comma 3.5 right parenthesis. All values are approximate.

Compare the estimated average rates of the graphed square root function over the interval [2,7]
to the estimated average rates of the cube root function y=x+2−−−−√3
over the same interval. To the nearest tenth, what is the difference between the estimated average rates of the graphed square root function and the estimated average rates of the cube root function?

(1 point)
The difference between the rates of change is
.

Answer 1

Average rate for graphed function = (3 − 2)/(7 − 2) = 1/5 = 0.2.

For y = ∛(x + 2): y(7) = ∛9 ≈ 2.0801, y(2) = ∛4 ≈ 1.5874, average rate = (2.0801 − 1.5874)/5 ≈ 0.0985.

Difference ≈ |0.2 − 0.0985| ≈ 0.1015 ≈ 0.1 (to the nearest tenth).

The difference is 0.1.