Grade 12 Math: Tangent Lines Worksheet
This worksheet focuses on understanding and calculating tangent lines for various functions, including using derivatives and applying concepts to circles and curves.
Includes
Standards
Topics
Grade 12 Math: Tangent Lines
Name:
Date:
Score:
Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Define a tangent line to a curve at a given point. How does it differ from a secant line?
2. The slope of the tangent line to a function at a point is given by the of the function at that point.
3. A line that is perpendicular to the tangent line at the point of tangency is called the line.
4. Which of the following statements about tangent lines is true?
A tangent line always intersects the curve at more than one point.
A tangent line is parallel to the curve at the point of tangency.
The slope of the tangent line is the instantaneous rate of change of the function.
Tangent lines only exist for linear functions.
5. Find the equation of the tangent line to the curve y = x² + 3x - 1 at the point (1, 3).
6. A circle has the equation x² + y² = 25. Find the equation of the tangent line to the circle at the point (3, 4).
7. If the derivative of a function at a point is zero, then the tangent line at that point is horizontal.
True
False
8. Find the point(s) on the curve y = x³ - 3x where the tangent line is parallel to the line y = 9x + 5.