1. What is Normal Slope?

In calculus, the normal slope refers to the slope of the line that is perpendicular to the tangent line at a given point on a curve. While the tangent line represents the instantaneous rate of change, the normal line is perpendicular to this tangent.

2. How Does the Calculator Work?

The calculator uses the normal slope formula:

Where:

• Tangent Slope — The slope of the tangent line at the point of interest
• Normal Slope — The resulting slope of the perpendicular normal line

Explanation: The negative reciprocal relationship ensures the normal line is perpendicular to the tangent line. If the tangent slope is zero (horizontal line), the normal slope becomes undefined (vertical line).

3. Importance of Normal Slope

Details: Normal lines are essential in various applications including physics (normal forces), computer graphics (surface normals), and optimization problems where perpendicularity is required.

4. Using the Calculator

Tips: Simply enter the tangent slope value. The calculator will compute the normal slope. Note that vertical tangent lines (undefined slope) will result in horizontal normal lines (zero slope).

5. Frequently Asked Questions (FAQ)

Q1: What if the tangent slope is zero?
A: A zero tangent slope (horizontal line) results in an undefined normal slope (vertical line).

Q2: What if the tangent slope is undefined?
A: An undefined tangent slope (vertical line) results in a zero normal slope (horizontal line).

Q3: How is this related to derivatives?
A: The tangent slope at a point is given by the derivative at that point, making this calculator useful after finding derivatives.

Q4: Can this be used in 3D space?
A: This calculator is for 2D curves. In 3D, normal vectors are used instead of slopes.

Q5: Why is the relationship negative reciprocal?
A: This ensures the product of the slopes is -1, which is the condition for perpendicularity in Cartesian coordinates.