Travel costs A simple model for travel costs involves the cost of gasoline and the cost of a driver. Specifically, assume gasoline costs $p/gallon and the vehicle gets g miles per gallon. Also assume the driver earns $w/hour.
b. At what speed does the gas mileage function have its maximum?

Verified step by step guidance

1. Identify the relationship between speed, gas mileage, and time. The gas mileage function typically decreases as speed increases beyond a certain point due to increased air resistance and engine efficiency changes.
2. Express the gas mileage function, g(v), in terms of speed v. This function will likely be a quadratic or similar function that models how gas mileage changes with speed.
3. Determine the critical points of the gas mileage function by taking the derivative of g(v) with respect to v and setting it equal to zero, g'(v) = 0.
4. Analyze the second derivative, g''(v), to confirm whether the critical points found are maxima or minima. A negative second derivative indicates a maximum.
5. Solve for the speed v at which the gas mileage function reaches its maximum by substituting the critical points back into the original gas mileage function.