how do you find a vertical tangent line of the function when x = (?)

(x^3) - xy + (y^3) = 10

Use implicite differentiation to get the derivative of the function, also re-arrange the original equation to make y the subject and sub that in for y in the differentiated equation. Now that you have the gradient function in terms of x, for a verticle tangent the denominator of the function has to be zero as the gradient is infinite. So find the values for x to make the denominator equal to zero and you have your x values, sub into original equation to find the y points and Voilà!! Hope that helps ;p