Most efficient speed of a car going uphill

When ignoring rolling resistance, acceleration, and optimum engine RPM, the most efficient uphill speed is the downhill coasting terminal velocity.

Derivation: Assume there is no rolling resistance so that the force against the car from friction is all air resistance.

F1 = cv^2

where c is the drag coefficient for given car and air conditions. The energy lost to air friction is:

E1 = dF1 = dcv^2 where d is the distance travelled.

The net work energy in reaching the top of the hill is:

E2 = mgh where h=d sin(angle)

The energy the engine must provide is:

E1 + E2 = dcv^2 + mgd sin(A).

Let d = t/v where t is time that d was travelled:

I want to find the v that minimizes E1+E2, so take the derivative with respect to v and set it to zero:

0 = tc - mgt/v^2 sin (A)

v = SQRT(mg sin(A) / c)

I can measure c by letting the car roll downhill. Let constant V be the terminal speed the car rolls downhill which is when the air resistance equals the force downward.

F1 = F2 = cV^2 = mg sin(A)

Solving for c and plugging into equation for F1 gives

v = V