C

Step 1: Identify the function represented in the given graph. The graph is of the function y = x², which is a standard parabolic curve opening upwards.
Step 2: Differentiate the function. To find \( \frac{dx}{dy} \), we first calculate \( \frac{dy}{dx} \):

• Given: \( y = x^2 \)
• Differentiate: \( \frac{dy}{dx} = 2x \)

Step 3: Solve for \( \frac{dx}{dy} \):

• Using the relation \( \frac{dx}{dy} = \frac{1}{\frac{dy}{dx}} \)
• So, \( \frac{dx}{dy} = \frac{1}{2x} \)

Step 4: Find the value of \( \frac{dx}{dy} \) at a specific point. Typically, you might evaluate it at point (0,0), but notice in this case it leads to a division by zero. Thus, evaluate at any other point, such as (1,1):

• At \( x = 1 \), \( \frac{dx}{dy} = \frac{1}{2(1)} = \frac{1}{2} \)

Conclusion: The value depends on the point we chose. If we say at (1, 1) the answer is \( \frac{1}{2} \). Therefore, option 'C' is stated as the solution.