SOLUTION: The fuel efficiency for a cetain midsize car is given by: E(v0 = -0.0235 v^2 + 2.768v - 53.85, where E(v) is the fuel efficiency in mpg for a car traveling v mph. What speed will

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Question 174318: The fuel efficiency for a cetain midsize car is given by: E(v0 = -0.0235 v^2 + 2.768v - 53.85, where E(v) is the fuel efficiency in mpg for a car traveling v mph. What speed will yield the maximum fuel efficiency, and what is taht max fuel efficiency?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Your function is a second degree polynomial in v, meaning that the graph of the function will be a parabola. Since the lead coefficient is less than zero, you have a parabola that is concave down and you know for sure that the vertex of the parabola is a maximum point.

For any parabola expressed in the form f%28x%29=ax%5E2%2Bbx%2Bc, the vertex is located at the point (-b%2F2a%29,f%28-b%2F2a%29).

All you need to do is calculate v%5Bmfe%5D=-b%2F2a=-2.768%2F%282%2A%28-0.0235%29%29 to determine the velocity that gives the maximum fuel efficiency and then evaluate the function for f%28v%5Bmfe%5D%29 to determine the fuel efficiency at that velocity.