Lost on Derivatives

Question

A laboratory study investigating the relationship between diet and weight in adult humans found that the weight of a subject, W, in pounds, was a function, W=f(c) of the average number of Calories, c, consumed by the subject in a day.

a. in the statement f(1500) = 145

what are the units of 1500? ____

what are the units of 145? ____

b. in the statement f '(2000) = 0

what are the units of 2000? ____

what are the units of 0? ____

c. in the statement f ^-1(154) = 2400

what are the units of 154? ____

what are the units of 2400? ____

d. what are the units of f '(c) = dW/dc

e. Suppose that Sam reads about f ' in this study and draws the following conclusion: If Sam increases his average calorie intake from 2800 to 2820 calories per day, then his weight will increase by approximately 0.4 pounds.

Fill in the blanks below so that the equation supports his conclusion.

f ' (________) = ________

Answer 1

Since W = f(c), where W is the weight in pounds and c is the number of calories consumed in a day

Then

a) f(1500) = 145 means that consuming 1500 calories per day causes a weight of 145 pounds.

[the units of 1500 are cal and 145 are lb]

b) f'(2000) = 0, means that consuming 2000 calories per day causes neither gain in weight nor loss in weight.

[the units of 2000 are cal and O is lb/cal]

c) f^-1(154) = 2400, means that a weight of 154 is caused by a consumption of 2400 calories per day.

[the units of 154 are lb and 2200 are cal]

d) f'(c) = dW/dc have units of pounds/calories

===> f'(c) = dW/dc [lb/cal]

e) Based on Sam's conclusion, f'(2800) = dW/dc = ΔW/Δc = 0.4/20 = 0.02

===> f'(2800) = 0.02