1. What is a Normal Line?

A normal line to a curve at a given point is the line perpendicular to the tangent line at that point. It's an important concept in calculus and geometry.

2. How Does the Calculator Work?

The calculator uses the normal line equation:

Where:

• \( f'(x_1) \) — Derivative (slope of tangent) at point \( x_1 \)
• \( (x_1, y_1) \) — Point on the curve
• \( -\frac{1}{f'(x_1)} \) — Slope of the normal line

Explanation: The normal line is perpendicular to the tangent, so its slope is the negative reciprocal of the tangent's slope.

3. Importance of Normal Lines

Details: Normal lines are used in physics (e.g., for reflection calculations), engineering (stress analysis), and computer graphics (lighting models).

4. Using the Calculator

Tips: Enter a differentiable function in terms of x and the x-coordinate of the point where you want the normal line.

5. Frequently Asked Questions (FAQ)

Q1: What if the tangent is horizontal?
A: Then the normal line will be vertical (undefined slope).

Q2: What if the tangent is vertical?
A: Then the normal line will be horizontal (slope = 0).

Q3: Can I use this for 3D surfaces?
A: This calculator is for 2D curves. 3D surfaces have normal vectors rather than normal lines.

Q4: What functions are supported?
A: In a full implementation, polynomial, trigonometric, exponential and logarithmic functions would be supported.

Q5: How accurate are the results?
A: Accuracy depends on proper function input and correct derivative calculation.