The weight, W, in lbs, of a child is a function of its age, a, in years, so W = f (a). (a) Do you expect f ′ (a) to be positive or negative? Why? (b) What does f (8) = 45 tell you? Give units for the numbers 8 and 45. (c) What are the units of f ′ (a) ? Explain what f ′ (a) tells you in terms of age and weight. (d) What does f ′ (8) = 4 tell you about age and weight? (e) As a increases, do you expect f ′ (a) to increase or decrease? Explain.

a) positive

b) the child is 45 lbs when she's 8 years old

c) lbs/year

d) The child increases 4 lbs/year when she's 8 years old

e) decrease

Step-by-step explanation:

a) Positive for the child because as they grow (age increases), a normal child should gain weight.

b) It tells that when age (years) = 8, the child weights 45 lbs

c) The unit of f' would be lbs/year. As it's a derivative of f (lbs) with respect to time t (years)

d) f' (8) = 4 tells us that the child weights increase at the rate of 4 lbs/year when she's 8 years old

e) As a increases f' (a) would decreases, as the rate of weight gain of a child would be slowing down as she grows.