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You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period.

Time (weeks)

0

1

2

3

4

5

6

7

8

Weight (lb)

150

144

143

141

140

137

137

132

129


During which time period is the average rate of change zero?

a.

From week 7 to week 8

b.

From week 3 to week 4

c.

From week 0 to week 1

d.

From week 5 to week 6

Verified Answer :

i think it's 5 to 6 but that's just my guess.

Answer:

The correct option is d.

Step-by-step explanation:

The average rate of change of a function between two points is defined as

\(m=\frac{f(x_2)-f(x_1)}{x_2-x_1}\)

If during a time period the average rate of change is zero, then

\(0=\frac{f(x_2)-f(x_1)}{x_2-x_1}\)

\(0=f(x_2)-f(x_1)\)

It means the value of the function is same for both the points.

From the given table it is clear that the weight is same for 5th and 6th week.

\(m=\frac{f(6)-f(5)}{6-5}\)

\(m=\frac{137-137}{1}\)

\(m=0\)

So, the average rate of change zero from week 5 to week 6.

Therefore the correct option is d.

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