This Question Is Confusing

Question

​Aki's Bicycle Designs has determined that when x hundred bicycles are​ built, the average cost per bicycle is given by C(x)=0.1x2−1.2x+5.758​, where​ C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per​ bicycle?

Answer 1

C(x) = 0.1x² − 1.2x + 5.758​

Find the derivative, set it equal to 0, and solve for x:

C'(x) = 0.2x - 1.2 = 0

x = 1.2 / .2 = 6

Now you know that there is either a maximum or minimum at x = 6. After plugging in 6, a value less than 6, and a value more than 6 into the original equation, you can determine that the minimum values occurs at x = 6. This means that building 6 bikes minimizes the average cost per bicycle.