Question

Chapter 8, Section 8.3, Question 014 Your answer is partially correct. Try again The table below gives the number of calories burned per minute, B f (w, 3), for someone roller blading, as a function of the person's weight, w, and speed, S. Calories burned per minute 11 mph 9.9 w\s 120 lbs 140 lbs 160 lbs 180 lbs 200 lbs 8 mph 9 mph 4.2 5.8 5 .1 6.7 6.1 | 7.7 7.0 8.6 7.9 9.5 10 mph 7.4 8.3 9.2 10.2 11.1 10.8 11.7 12.6 (a) is positive or negative? Is f positive or negative? What do your answers tell us about the effect of weight and speed on calories burned per minute? is positive Jis positive

Answer 1

Answer

The table gives the value of the number of calories burned per minute B as a function of the person's weight w and speed s.

From the table, we can determine the signs of the partial derivatives w.r.t. w and s.

For a constant speed s, the value of B increases as w increases.

Hence, $\small f_w$ is positive.

For a constant weight w, the value of B increases as speed s increases.

Hence, $\small f_s$ is positive.

$\small f_w(160,10)\approx \frac{f(160,10)-f(140,10)}{160-140} =\frac{9.2-8.3}{20}=\frac{0.9}{20}=0.045$

$\small f_s(160,10)\approx \frac{f(160,10)-f(160,9)}{10-9} =\frac{9.2-7.7}{1}=1.5$

Hence,

$\small f_w$ is positive.

$\small f_s$ is positive.

A heavier person will burn more calories per minute while roller-blading than a lighter person.

The number of calories burned per minute while roller-blading goes up as the speed goes up.

$\small f_w(160,10)=0.045$

$\small f_s(160,10)=1.5$

The number of calories increases by about 0.045 if the weight is increased by 1 pound.

The number of calories increases by about 1.5 if the speed is increased by 1 mph.