MATH 275 Lecture Notes - Lecture 9: Product Rule
1 Oct 2016
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He next goes on to give the geometric definitions of derivative and slope but unfortunately i cannot draw precise graphs on here. I will just tell you the definitions. m= slope m sec = normal line means perpendicular to tangent so to find the tangent slope take the negative reciprocal of normal lines slope. For finding all equations of tangent lines at a point say (1,-3) that does not touch the curve (plug in x = 1 to see if. 3 is y to test, if not it does not touch) use the rise/run formula above and (x1,y1) is your given point so (1,-3) and x2,y2 is just x and the function so ex. (x, 4x^3- 10x+7). m is computed by deriving the function. Equate the two and solve for x and plug those x values into the derived function to get slopes. Now use those slopes for point slope form to get all equations.
