Question

The function C(m) = -.41m^2 + 6.7m - 44/ .7m represents Miles Traveled per lb. of CO 2
released as a function of speed(in MPH) for a hyundai Sontana. the domain of this function is [10,90].

A) calculate C'(m)

B)find the critical points of C(m).

C)Where does C(m) have global max(s) and min(s)

D) which speed maximizes miles traveled per pound of CO 2

F) at which speed do you think the highway speed limit should be set? why?

(Guys im totally unsure how to start the problem due to the fact its division in it )

Answer 1

I assume that you mean

C(m) = (-.41m^2 + 6.7m - 44)/.7m
As you recall from Algebra I, that is

C(m) = (1/.7)(-.41m + 6.7 - 44/m)
so,
C'(m) = (1/.7) (-.41 + 44/m^2)
= (1/.7)(44-.41m^2)/m^2

Since the denominator is always positive, C'(m)=0 when

44-.41m^2 = 0
m^2 = 44/.41
m = ±10.36

Now, if you really did mean what you typed, then C(m) is even easier, since only the last term is divided by m.

You could have used the quotient rule to get C'(m), but why bother, when a simple division simplifies things from the start?