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?
I suspect m represents speed, not miles
and that C is miles per pound
but what does 44/.7m mean?
44 gord with the top part
gord? Isn't that an intestinal disorder?
Is your formula
-.41 m^2 + 6.7 m - 44 ??????
or what
if so part a is
dC/dm = -.82 m + 6.7
that is zero when m = 6.7/.82 which is part b
part c include end points
check at m = 10 and m = 90 as well as the parabola vertex at 6.7/.82
Obviously travel at m = 6.7/.82, the vertex at the top of this parabola, maximum miles for a pound ofCO2
To solve the given problem, we will first find the derivative of the function C(m). Let's proceed step-by-step:
A) To calculate C'(m), apply the power rule and the constant multiple rule of differentiation to each term in the function:
C(m) = -0.41m^2 + 6.7m - 44 / 0.7m
C'(m) = dC(m)/dm = [d(-0.41m^2)/dm] + [d(6.7m)/dm] + [d(-44/0.7m)/dm]
Using the power rule, we differentiate each term and simplify:
C'(m) = -0.82m + 6.7 + 44/(0.7m^2)
So, C'(m) = -0.82m + 6.7 + (44/0.7m^2)
B) To find the critical points, set C'(m) equal to zero and solve for m:
-0.82m + 6.7 + (44/0.7m^2) = 0
Solving this equation will give you the critical points.
C) To find the global maximum(s) and minimum(s) of C(m), you need to check the endpoints of the domain [10, 90] and the critical points found in step B. Evaluate C(m) at these values and compare to find the highest and lowest points.
D) To find the speed that maximizes miles traveled per pound of CO2, you need to find the maximum point(s) of C(m) by comparing the values obtained in step C.
E) To determine the suitable highway speed limit, there are different factors to consider, such as fuel efficiency, emissions, safety, and local regulations. In this case, we are only given the function C(m) representing miles traveled per pound of CO2. However, we would need additional information on these other factors to make an informed recommendation on setting the highway speed limit.