To find the point on the curve where the second derivative of y with respect to x is equal to zero, we need to solve the equation d^2y/dx^2 = 0.
The second derivative of y with respect to x is given by:
d^2y/dx^2 = y^3(250xy - 75) / ((5xy - 1)^3)
Setting this equal to zero, we have:
y^3(250xy - 75) / ((5xy - 1)^3) = 0
To find the point where this equation is satisfied, we can set each term equal to zero individually.
First, setting y^3 = 0, we obtain:
y = 0
Next, setting (250xy - 75) = 0, we solve for x:
250xy = 75
xy = 75/250
xy = 3/10
x = (3/10y), where y is NOT equal to zero
Therefore, the point (x, y) where d^2y/dx^2 = 0 is given by:
(x, y) = ((3/10y), 0), where y ≠0
Note: This point is a critical point on the curve, indicating a possible point of inflection.