I apologize for that. I didn't realize I didn't write the whole problem. Thank you for pointing that out to me.
Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by c(x) =0.1x^2 -0.5x+ 9.295. Where C(x) is in hundreds of dollars, how many bicycles should the shop build to minimize the average cost per bicycle?
Thank you for your help
To find the number of bicycles that will minimize the average cost per bicycle, we need to find the minimum point on the cost function.
To minimize a quadratic function like c(x) = 0.1x^2 - 0.5x + 9.295, we can use calculus. The first derivative of the function will help us find critical points.
The derivative of c(x) with respect to x is given by:
c'(x) = 0.2x - 0.5
To find the critical point, we set the derivative equal to 0 and solve for x:
0.2x - 0.5 = 0
0.2x = 0.5
x = 0.5 / 0.2
x = 2.5
Now, we need to determine whether this critical point is a minimum or maximum. To do this, we can use the second derivative test.
The second derivative of c(x) is:
c''(x) = 0.2
Since the second derivative is positive, we know that the critical point is a minimum.
Therefore, the number of bicycles Aki's Bicycle Designs should build to minimize the average cost per bicycle is x = 2.5 hundred bicycles.