The answer is 1.5lb/month; 0.58lb/month; 1.25lb/month lim r t h)-) 4. Under what

Question

The answer is 1.5lb/month; 0.58lb/month; 1.25lb/month lim r t h)-) 4. Under what conditions does a function fail to have a deriv- ative at a number? Illustrate your answer with sketches. 9.3 Exercises I. AVERAGE WEIGHT OF AN INFANT The following graph shows the weight measurements of the average infant from the time of birth (t0) through age 2 ( 24). By comput- ing the slopes of the respective tangent lines, estimate the rate of change of the average infant's weight when 3 and when t 18. What is the average rate of change in the average infant's weight over the first year of life? 30 3.5 T1 22.5 20 7.5 5 10 o 7.5 2 4 6 8 10 12 14 16 18 20 22 24 Months 2. FORESTRY The following graph shows the volume of wood produced in a single-species forest Here

Explanation / Answer

When asked to find the average rate of change, this translates mathematically to "find the slope". Find the slope between the points.

Unfortunately, we can't use (y1-y2)/(x1-x2) because we can't easily identify y1 and y2. The problem tells us to compute the slopes of the tangent lines.
Tangent line to 3, f(3) is 7.5/5=3/2
Tangent line to 18, f(18) is 3.5/6=7/12
If we average these two tangent lines, the answer that results will be the approximate slope between these lines.
((3/2)+(7/12))/2=25/24

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