Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that . Find M (30), M (70)and M (95).
A)M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051
B)M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051
C)M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051
D)M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0
E)M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049

Question

Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that  . Find M (30), M (70)and M (95).
A)M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051 
B)M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051 
C)M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051 
D)M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0 
E)M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049

Quizplus · Accepted Answer

The problem provides us with the values of M'(x) at x = 30, 70, and 95. To find the actual values of M(x), we need to integrate M'(x) with respect to x. However, we are not given the value of M(x) at any specific speed, so we cannot find the constant of integration. Therefore, we can only determine the relative values of M(x) at different speeds, rather than the absolute values.

Since M'(30) = 0, we know that M(30) is a local maximum or minimum of the function, but we cannot determine which one without more information. Similarly, M'(95) is negative, so we know that M(95) is decreasing as x increases, but we cannot determine the exact rate of decrease.

The only value of M'(x) that we can use to compare the different speeds is M'(70), which is positive. This tells us that as x increases from 70, M(x) is increasing at a rate of 0.0049 miles per gallon per mile per hour. Therefore, M(70) must be less than both M(30) and M(95), since they are both either at a local maximum/minimum or decreasing.

Thus, the best choice is C: M'(30) = 0.0049, M'(70) = 0, M'(95) = -0.000051.

Your Porsche S Gas Mileage (In Miles Per Gallon)is Given