Question: For speeds between 40 and 65 miles per hour, a truck gets 300/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs $1.12 per gallon, and the driver is paid $12 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck? Assume that the distance he travels is 400 miles, and let t=time it takes him to drive the 400 miles. You must minimize the total cost of gasoline plus the drivers pay for the trip. As usual, x miles per hour is the independent variable.

Target function f(x):

Domain of f(x)_ _____
Domain of f(x)__________
Exact value of 2nd derivative at critical value of x=_________
Max. or Min. value of f(x)__ _______