University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2024
Views:

69

Pages:

5
Author:

McGowanfgu

Honors Pre-Calculus [Day 1] Definition of a Tangent Line NOTES Given the graph of 𝑓(𝑥) = 𝑥 2 , draw a tangent line to the graph at (1, 1). What does the slope of that line appear to be? Why is it difficult to get the slope of a tangent line in this manner? Finding the slope of the tangent line at (1, 1) Find the equation of the tangent line in the example above: Definition of a Tangent Line Name: Example 1: Find the slope of the tangent line to the graph 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 3 at (2, 5) Example 2: Find the equation of the tangent line in Example 1 Example 3: Find the slope of the tangent line to the graph 𝑓(𝑥) = Example 4: Find the equation of the tangent line in Example 3 3 𝑥 at (3, 1) Example 5: Find the slope of the tangent line to the graph 𝑓(𝑥) = −2𝑥 + 5 at (2, 1) Example 6: Find the equation of the tangent line in Example 5 Example 7: Find the slope of the tangent line to the graph 𝑓(𝑥) = √𝑥 + 1 at (3, 2) Example 8: Find the equation of the tangent line in Example 7 Honors Pre-Calculus [Day 1] Definition of a Tangent Line HOMEWORK Name: Find an equation of the tangent line to the curve at the given point. 1. 𝑓(𝑥) = 5 − 2𝑥 at (− 3, 11) 2. 𝑓(𝑥) = 1 + 2𝑥 − 3𝑥 2 at (1, 0) 3. 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 3 at (2, −1) 4. 𝑓(𝑥) = 3𝑥 − 4 at (3, 5) 5. 𝑓(𝑥) = √𝑥 at (9, 3) 6. 𝑓(𝑥) = 1 𝑥2 at (− 1, 1) 1 7. 𝑓(𝑥) = 𝑥 2 − 5 at (2, − 1) 8. 𝑓(𝑥) = 𝑥 at (−1, −1) 9. 𝑓(𝑥) = √1 + 2𝑥 at (4, 3) 10. 𝑓(𝑥) = 1. 𝑦 − 11 = −2(𝑥 + 3) or 𝑦 = −2𝑥 + 5 2. 𝑦 = −4(𝑥 − 1) 3. 𝑦 = −1 4. 𝑦 − 5 = 3(𝑥 − 3) or 𝑦 = 3𝑥 − 4 5. 𝑦−3= 6. 𝑦 − 1 = 2(𝑥 + 1) or 𝑦 = 2𝑥 + 3 7. 𝑦 + 1 = 4(𝑥 − 2) or 𝑦 = 4𝑥 − 9 8. 𝑦 + 1 = − (𝑥 + 1) or 𝑦 = −𝑥 − 2 9. 𝑦−3= 10. 𝑦 − = − (𝑥 − 4) or 𝑦 = − 𝑥 + 1 1 6 1 3 (𝑥 − 9) or 𝑦 = (𝑥 − 4) or 𝑦 = 1 6 1 3 𝑥+ 𝑥+ 3 2 5 3 2 𝑥 at (4, 1 ) 2 or 𝑦 = −4𝑥 + 4 1 1 1 2 8 8