Calculus 1000A/B Lecture Notes - Lecture 1: Tangent, Polynomial

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Rasul Shafikov

Document Summary

Linear functions are of the form y = mx + b. Characteristics: polynomial of degree 1, graph is a straight line, m is the slope, b is the y intercept. Example: find the linear function that passes through the points (-1, -1) and (2, 5). Express your answer in slope-intercept, point-slope, and general form. General form: ax + by + c = 0 m = (5) ( 1) (2) ( 1) = 2 , so y 5 = 2(x 2) using (2, 5) as the point. We can rearrange the equation to get slope-intercept and general as y = 2x + 1 and. 2x y + 1 = 0 , respectively. Find the equation of a tangent to the curve. The problem is that we only have one point, so determining the slope will be difficult. Since y = x 2 the slope formula becomes m = x 2 4 x 2.