J's bike has determined that when x hundred bikes are built, the average cost per bike is given by C(x)= 0.1x^2-1.2x+4.993, where C(x) is in hundreds of dollars. how many bikes should the shop build to minimize the average cost per bike?

C(x) is just a parabola, with minimum value at

x = 1.2/0.2 = 6

so, 600 bikes will minimize the average cost per bike

thanks Steve if I was to figure avg cost

3.6-7.2+4.493=.893 times 100
for a total of $89.30 per bike??

To minimize the average cost per bike, we need to find the value of x that corresponds to the minimum point of the function C(x).

In this case, C(x) = 0.1x^2 - 1.2x + 4.993 is a quadratic function.

To find the minimum point of a quadratic function, we can use the vertex formula. The vertex formula states that the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by x = -b/2a.

In our case, a = 0.1, b = -1.2, and c = 4.993. Plugging these values into the formula, we have:

x = -(-1.2) / (2 * 0.1)
x = 1.2 / 0.2
x = 6

Therefore, the value of x that corresponds to the minimum point of the function is 6.

So, the shop should build 600 bikes (since x is in hundreds) to minimize the average cost per bike.