MATH114 Lecture Notes - Lecture 17: Linear Approximation, Lincoln Near-Earth Asteroid Research, Maxima And Minima

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

Document Summary

Math 114 lecture 17 linear approximation. Idea: have y = f(x), complicated functions near a point a, tangent line is a good approximation for f(x). Equations for tangent line y =l(x) at x = a y y1 = m(x x1) y = f(a) + f"(a)(x a) Linear approximation says f(x) f(a) + f"(a)(x a) if x is near a. Take f(x) = (cid:1876) , a = 100. Linear approximation method says if x is near 100. Can get dy = change in tangent line. Note that dy is the same as df. Slope of the tangent line in the graph is f"(x) Want: f = f(x + x) f(x) change in f. Upshot: if dx is small then (cid:1877) (cid:1877) Example: go back to (cid:883)(cid:882)(cid:883) x = 100, want (cid:1877)= (cid:883)(cid:882)(cid:883) (cid:883)(cid:882)(cid:882) f(x) = (cid:1876) (cid:883)(cid:884) (cid:883)(cid:882)(cid:882)(cid:1876)=(cid:883)(cid:884)(cid:882)=(cid:882). (cid:882)5 (cid:1877)= Note that dx is change in x (101 100) Example: f(t) = temperature at time domain = 2017 t in edmonton.