Question

The quantity, Q mg, of nicotine in the body t minutes after a cigarette is smoked is given by Q = f(t).
a) Interpret the statements f(10) = 0.65 and f '(10) = -0.02 in terms of nicotine. What are the units of the numbers 10, .065, -0.02?
Units for : 10________, 0.65 _______, -0.02 _________
f(10) = 0.65 means
f '(10) = -0.02 means

b) Use the information given in part (a) to estimate f(11).

Answer 1

you know, you could always just update your first post, rather than starting a whole new thread. Just sayin' ...

so, what's to interpret?
They told you "The quantity, Q mg, of nicotine ..."
so f(10) is the amount after 10 minutes (mg)
f'(10) is the rate at which Q is changing (mg/min)

since ∆f/∆t ≈ df/dt for small ∆t,
f(11) ≈ f(10) + f'(10)*1 = 0.65 - 0.02 = 0.63