Lesson 2 1 Tangent and Velocity Problems Transparency

Lesson 2 -1 Tangent and Velocity Problems

Transparency 1 -1 5 -Minute Check on Algebra 1. 6 x + 45 = 18 – 3 x 2. x 2 – 45 = 4 3. (3 x + 4) + (4 x – 7) = 11 4. (4 x – 10) + (6 x +30) = 180 5. Find the slope of the line k. y k (6, 4) (0, 1) 6. (-6, -2) Find the slope of a perpendicular line to k Standardized Test Practice: A 1/2 B 2 C -1/2 D -2 Click the mouse button or press the Space Bar to display the answers. B A C x

Transparency 1 -1 5 -Minute Check on Algebra 1. 6 x + 45 = 18 – 3 x 9 x +45 = 18 2. x 2 – 45 = 4 x² = 49 3. (3 x + 4) + (4 x – 7) = 11 7 x - 3 = 11 4. (4 x – 10) + (6 x +30) = 180 10 x + 20 = 180 9 x = -27 x = √ 49 x = +/- 7 7 x = 14 x=2 10 x = 160 5. Find the slope of the line k. (0, 1) (-6, -2) Find the slope of a perpendicular line to k 1/2 B 2 C -1/2 D k (6, 4) Standardized Test Practice: A x = 16 y ∆y y 2 – y 1 4– 1 3 1 m = ----------- = ---∆x x 2 – x 1 6– 0 6 2 6. x = -3 -2 Click the mouse button or press the Space Bar to display the answers. B A ∆x ∆y C x

Objectives • Understand the tangent problem • Understand the velocity problem

Vocabulary • Tangent – a line that touches the curve in only one point; same slope as curve at intersection point • Secant – a line that intersects the curve in only two points; average slope (rate of change) between two points • Average Velocity – distance traveled divided by time elapsed average of two instantaneous velocities; the slope of the secant line • Instantaneous Velocity – the velocity at an instant in time; limit of average velocity as the two points of the secant get closer together (as ∆x → 0) the slope of the tangent line

Slope rise ∆y d-b m = ---------- = rate of change of y with respect to x run ∆x c-a y y = f(x) Secant Line Q (c, d) P (a, b) x Tangent Problem: • Slope of a curve at any point (slope of a tangent at that point) can be estimated by taking the slope of the secant line with those two x-values (a and c) being very close together

Summary & Homework • Summary: – Two points determine a line – Three noncollinear points determine a plane • Homework: pg 9, 10: 7 -8, 13, 15, 17, 22 -23, 32, 34 -35