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)

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

d

step-by-step explanation: