How many bicycles should we build?

Question

Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.8x^2-1.7x+8.716, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? Round to the nearest integer.

Answer 1

That's just a function. If you remove the C(x), then you can just use quadratic formula to solve for the rest

Answer 2

on differentiating,

C'(x)=1.6x-1.7

on differentiating

C''(x)>0

Now, C'(x)=0 gives x approximately equals to 1

So, the answer is 1

Answer 3

C'=0

=> 1.6x-1.7=0

=> x=1.0625

Subst into C(x) and press calculator.