Published by:
CGP EDU Academic Team
Published on: September 12, 2026
What is the value of 
, for the following graph?
Text Solution
Verified by ExpertsThe correct answer is:
C
Step 1: The function given is y = x^2.
Step 2: To find \frac{dx}{dy}, first compute \frac{dy}{dx}.
\frac{dy}{dx} = 2x.
Step 3: Using the relationship \frac{dx}{dy} = \frac{1}{\frac{dy}{dx}}:
\frac{dx}{dy} = \frac{1}{2x}.
Step 4: At the point (0, 0), substituting x = 0 into \frac{dx}{dy} gives: \frac{dx}{dy} = \frac{1}{2(0)}.
Step 5: This indicates that at the point (0, 0), \frac{dx}{dy} is undefined or infinite, leading us to conclude that the vertical tangent at this point signifies vertical behavior of the curve.
Therefore, for this graph, \frac{dx}{dy} does not attain a finite value.
Step 2: To find \frac{dx}{dy}, first compute \frac{dy}{dx}.
\frac{dy}{dx} = 2x.
Step 3: Using the relationship \frac{dx}{dy} = \frac{1}{\frac{dy}{dx}}:
\frac{dx}{dy} = \frac{1}{2x}.
Step 4: At the point (0, 0), substituting x = 0 into \frac{dx}{dy} gives: \frac{dx}{dy} = \frac{1}{2(0)}.
Step 5: This indicates that at the point (0, 0), \frac{dx}{dy} is undefined or infinite, leading us to conclude that the vertical tangent at this point signifies vertical behavior of the curve.
Therefore, for this graph, \frac{dx}{dy} does not attain a finite value.
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