MATH114 Lecture Notes - Lecture 10: Third Derivative, Second Derivative, Endorphins

• School: University of Alberta
• Department: Mathematics
• Course: MATH114
• Professor: Alsaody,Seidon

Document Summary

Math 114 lecture 10 the derivative. Idea: measure instantaneous rate of change of a function. Application: speed of a car (rate of change of displacement). Geometrically, it is the slope of the tangent line. https://slideplayer. com/slide/5296642/ General remarks: line through point (a,b) then any point on the line satisfies. Definition: the tangent line to the curve y = f(x) at (a,f(a)) is the line through (a, (f(a)) with. Slope of the tangent line is (cid:3052) (cid:3051)=(cid:4666)(cid:3051)(cid:4667) (cid:4666)(cid:3028)(cid:4667) (cid:3051) (cid:3028) (cid:3052) (cid:3029)(cid:3051) (cid:3028)=, equation y b = m(x-a) slope = lim(cid:3051) (cid:3028)(cid:4666)(cid:3051)(cid:4667) (cid:4666)(cid:3028)(cid:4667) (cid:3051) (cid:3028) Example: find the equation of the tangent line to y = x2 at (2,4) So tangent line: slope is 4 through (2,4) Equation: y 4 = 4(x-2) y = 4x-2. Note: if line has slope m, perpendicular line has slope -1/m (cid:3051) (cid:2870) =lim(cid:3051) (cid:2870)(cid:4666)(cid:3051) (cid:2870)(cid:4667)(cid:4666)(cid:3051)+(cid:2870)(cid:4667) (cid:3051) (cid:2870) =lim(cid:3051) (cid:2870)(cid:1876)+(cid:884)=(cid:886: find the equation of the line through (2,4) perpendicular to the tangent.