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.

Question

Quizplus · Accepted Answer

To minimize the total cost, we need to minimize the fuel consumption rate function $G(x)$. The function $G(x)$ is minimized when its derivative is zero. Solving for $x$ gives approximately 56.0 mph.

Solve the Problem G(x)=135(64x+x49)G(x)=\frac{1}{35}\left(\frac{64}{x}+\frac{x}{49}\right)G(x)=351​(x64​+49x​) While Traveling At xmphx \mathrm{mph}xmph If Fuel Costs

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