Answer: The minimum average cost per dulcimer = $ 180
The number of dulcimers should be built to achieve that minimum =150
Step-by-step explanation:
Given : A company has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by
, where C(x) is in hundreds of dollars.
Now, differentiate the above function with respect to x, we get
(1)
Put C'(x) =0, we get

Again differentiate (1) w.r.t. x , we get
By second derivative test , we have the value of x where C(x) is minimum=1.5

Hence, the minimum average cost per dulcimer = $ 180
The number of dulcimers should be built to achieve that minimum =150