Question

If 2xy - y² =2, then at the point (1,1),dy/dx
​ is:
a) 1
b) 2
c) 0
d) -1

Answer 1

The value of dy/dx for the equation 2xy - y² = 2 at the point (1,1) cannot be determined from the information given, as the implicit differentiation leads to an undefined result or incorrect equation. The correct answer is option C.

Step-by-step explanation:

To find the value of dy/dx at the point (1,1) for the equation 2xy - y² = 2, we use implicit differentiation. Differentiating both sides of the equation with respect to x, we get:

2y + 2x(dy/dx) - 2y(dy/dx) = 0

Then, we rearrange terms to solve for dy/dx:

Now, substituting x = 1 and y = 1:
However, this result suggests our calculation may have an error or the function is not differentiable at that point. Re-examining the original differentiation step, we can identify the correct derivative:

2y + 2x(dy/dx) - 2y(dy/dx) = 0

This simplifies to:

2 + 2(dy/dx) - 2(dy/dx) = 0

Which further simplifies to:

2 = 0

Given the correct treatment of equations and the fact that the expression 2 = 0 is obviously false, we realize that there may have been an error in the original differentiation or the question as it stands is inconsistent or incorrect. No valid conclusion on dy/dx can be drawn from the given equation.