MAT157Y1 Lecture : Slope.pdf

• School: UTSG
• Department: Mathematics
• Course: MAT157Y1
• Professor: Dan Dolderman

Document Summary

The key to this question is to try to calculate the slope of the tangent in two di erent ways. (cid:16) (cid:17) Given a tangent line that passes though the point (1, 2), suppose that it. Our goal is to nd what touches the curve at the point of tangency a could be. a, a a+1. 1 (x+1)2 (cid:16) a, a a+1 (cid:17: second, remember that two points on the tangent line are (1, 2) and. So we can calculate the slope using these two points: Check that this simpli es to a+2 (a+1)(1 a) (exercise). So now we just have to equate these two slopes: Multiply out and simplify: (a + 1)(1 a) = (a + 2)(a + 1)2 (1 a) = (a + 2)(a + 1) if we divide out by a factor of (a + 1). To nish, expand the right hand side and collect like terms.