A truck has a min. speed of $9mph$ in the highest gear. When traveling $x$ mph, the truck burns diesel fuel at a rate:

$0.0224868((1156/x) + x)$ gal/mile

The truck can not be driven over $51mph$ and the diesel fuel costs $1.44 gal, find the following.

(a) The steady speed that will minimize the cost of diesel fuel for a 470 mile trip.

The answer for (a) is 34 mile/hour, this is the min. of the function above found via the Extreme Value Theorem.

***This is where I am having trouble:***

(b) Find the steady speed that will minimize the cost of a 470 mile trip when the driver is being paid $17/hour.

* I have found out that total cost = (cost of the driver) + (cost of fuel for the trip)

I have yet to put any real work behind this because I am lost and I do not know where to start to figure this problem out. I could try a bunch of values, but that would not work and take so long. I thought about making the bounds [34, 51] and somehow finding the inflection point on that, but I do not believe that would work.

I'd appreciate some help with this problem. Thanks.