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Question
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of \[\frac{dx}{dy}\] ?
Solution
Slope of the y-axis is \[\infty\] .
Also, the tangent at (x, y) on the curve y = f(x) is parallel to the y-axis,
∴ Slope of the tangent, \[\frac{dy}{dx}\] = Slope of the y-axis = \[\infty\]
\[\frac{dx}{dy} = \frac{1}{\left( \frac{dy}{dx} \right)} = \frac{1}{\infty} = 0\] .
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