if someone could answer this problem, I will bow down to you like a god?

Question

If data collected of CO, plotting the data and fitting a curve to the resulting scatter plot yielded the function COs(x)=e^-2.465+0.028x, where x is the speed in miles per hour. The units for CO2(x) are grams per second (g/sec). Convert the CO to grams/mile, then determine the speed that minimizes the CO in terms of grams/mile.
grams/second(conversion factors)=(grams per mile)

If you can answer this in the next 30-40 minutes, I will bow to you. I need this solution for extra credit, and i spent 2 hours on it last night. Please Help, It would really be appreciated.

thats how it is in the book
crazy huh

Answer 1

well, here's a few pointers:

if cos(x) = exp(2.465 + 0.28x) then one can use some algebra and the fact (sin(x))^2 + (cos(x))^2 = 1 ....

(cos(x))^2 = (exp(2.465 + 0.28x))^2
(cos(x))^2 + (sin(x))^2 = (exp(2.465 + 0.28x))^2 + (sin(x))^2
1.00 = (exp(2.465 + 0.28x))^2 + (sin(x))^2

now, since (x^a)^b = x(a+b) :

1.00 = exp(2.465 + 0.28x + 2) + (sin(x))^2
1.00 = exp(4.465 + 0.28x) + (sin(x))^2

Next, take the first derivitive of this function in terms of x :

d/dx(exp(4.465 + 0.28x) + (sin(x))^2) -1) =
d/dx(exp(4.465 + 0.28x)) + d/dx((sin(x))^2)) - 0

(the constant term drops out because d/dx(1) = 0)

Now, set the resulting function above equal to zero. Solve for x. This gives the point on the curve where the slope is zero. Such a point is either a maximum or a minimum. I believe taking the second derivitive is the way of determining whether the point is a maximum or minimum. It is based on whether the function gives a positive or negative answer when the minimum point is input. Consult your math book for the formulas related to derivitives of expoential and trigometric functions. Once you have determined the minimum point, then apply conversion factors.

Hope this helps.

Answer 2

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Answer 3

I don't understand. You have y=f(x), where x is in miles per hour. Then y must also be in miles per hour; it can't be grams per second.

Answer 4

The problem appears to involve diffrientiation but pls review and restate it properly

Answer 5

Are you sure you have stated this problem correctly?