Solve the Problem $G(x)=\frac{1}{35}\left(\frac{64}{x}+\frac{x}{49}\right)$ While Traveling At $x \mathrm{mph}$ If Fuel Costs

Multiple Choice

Solve the problem.
-A truck burns fuel at the rate (gallons per hr) of $G(x) =\frac{1}{35}\left(\frac{64}{x}+\frac{x}{49}\right)$ while traveling at $x \mathrm{mph}$ . If fuel costs $\$ 1.27$ per gallon, find the speed that minimizes total cost for a 200 -mile trip. Round to the nearest tenth.

A) $49.5 \mathrm{mph}$
B) $56.5 \mathrm{mph}$
C) $56.0 \mathrm{mph}$
D) $62.2 \mathrm{mph}$