Explain all work, show your steps as well as your reasoning. You should write what you are doing and why. The person reading your solutions should be able to understand what you have done because you explained it in words. Submissions with little or no written explanations will not receive full marks.

1. (5 points) Suppose that the fuel efficiency E (in km/L) of a certain car can be modeled by 100 E = v + 0.1(v - 80)2 + 0.5(T - 20)2' where u is the velocity (in km/h) and T is the outside temperature (in C). Suppose the temperature is constant. Use a derivative to illustrate how fuel efficiency changes if velocity changes. (Which derivative do you need to find?) Then evaluate your derivative if u - 90 km/h and 7 - 20C and explain what the sign of this derivative means in the context of this