1. What is Point Of Tangency Calculus?

Point of tangency calculus refers to finding the point where a line is tangent to a curve. For quadratic functions, this occurs when the discriminant equals zero, indicating exactly one real solution.

2. How Does the Calculator Work?

The calculator uses the discriminant formula:

Where:

• \( a \) — Coefficient of x²
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: When discriminant equals zero, the quadratic equation has exactly one real root, indicating the point of tangency.

3. Importance of Discriminant Calculation

Details: Calculating the discriminant helps determine the nature of roots for quadratic equations and identifies points of tangency between curves and lines.

4. Using the Calculator

Tips: Enter coefficients a, b, and c from your quadratic equation (ax² + bx + c = 0). The calculator will determine if discriminant equals zero and find the point of tangency.

5. Frequently Asked Questions (FAQ)

Q1: What does discriminant = 0 mean geometrically?
A: It means the quadratic curve touches the x-axis at exactly one point, indicating a point of tangency.

Q2: Can discriminant be negative?
A: Yes, a negative discriminant indicates no real roots and no points of tangency with the x-axis.

Q3: What is the significance of point of tangency?
A: It represents the point where a line just touches a curve without crossing it, important in optimization and geometry problems.

Q4: Does this work for all types of curves?
A: The discriminant method specifically applies to quadratic functions. Other curves require different calculus methods to find tangency points.

Q5: How is this related to derivatives?
A: For general curves, points of tangency are found by setting the derivative equal to the slope of the tangent line.