The day with the most babies delivered in August is approximately the 1.14th day of the month, which falls between the 1st and 2nd of August.
The function F(x) = (x³/3930000) - (x²/1805) + (1024896x/29556875) + (1/31) represents the average number of babies delivered in August on a given day x. To determine the day with the most deliveries, we need to find the maximum value of F(x).
Taking the derivative of F(x) with respect to x, we get:
F'(x) = (x²/3930000) - (2x/1805) + (1024896/29556875)
Setting F'(x) = 0 and solving for x, we find x ≈ 1.14. This means that the day with the most babies delivered in August is approximately the 1.14th day of the month, which falls between the 1st and 2nd of August.
To confirm that this is indeed the maximum, we can evaluate F(x) at nearby values of x. For instance, F(1) ≈ 0.001106, F(2) ≈ 0.001162, and F(3) ≈ 0.001099. As you can see, F(x) reaches its maximum value at approximately x = 1.14.
Therefore, the day with the most babies delivered in August is approximately the 1.14th day of the month, which falls between the 1st and 2nd of August.