Write the value of `(dy)/(dx)`, if the normal to the curve `y=f(x)` at (x, y) is parallel to y - axis.

Answer

To find the value of \(\frac{dy}{dx}\) when the normal to the curve \(y = f(x)\) at the point \((x, y)\) is parallel to the y-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Normal Line**:
- The normal to a curve at a given point is a line that is perpendicular to the tangent at that point.

2. **Normal Parallel to the y-axis**:
- If the normal line is parallel to the y-axis, it means that the slope of the normal line is undefined (or infinite). This occurs when the tangent line at that point has a slope of 0.

3. **Slope of the Tangent**:
- The slope of the tangent line to the curve at the point \((x, y)\) is given by \(\frac{dy}{dx}\).
- If the normal is vertical (parallel to the y-axis), the slope of the tangent line must be 0.

4. **Setting Up the Equation**:
- Since the slope of the tangent line is 0, we can write:
\[ \frac{dy}{dx} = 0 \]

5. **Conclusion**:
- Therefore, the value of \(\frac{dy}{dx}\) when the normal to the curve at the point \((x, y)\) is parallel to the y-axis is:
\[ \frac{dy}{dx} = 0 \]

### Final Answer:
\[ \frac{dy}{dx} = 0 \]