Determine the point(s) at which the graph of y^6=y^4-x^4 has a vertical tangent.

Step-by-step explanation:

We will first find the derivative of the function to get the formula for the slope of the tangent.  Using implicit differentiation, we find that:

and

 Solving for the derivative and at the same time simplifying within the parenthesis:

so

If our tangent line is vetical, that means that the slope is undefined.  Our slope is undefined where y = 0.  Therefore, we need to find x when y = 0 in our original equation.  If y = 0, then

becomes

and

That means that x = 0 (we divide away the negative on the x, and since 0 isn't negative or positive, we get that x^4 = 0)

That means that the point at which the tangent is vertical is (0, 0)

a

step-by-step explanation: