MAT 1320 Lecture 20: mat1320E-2018-notes20-filled-in

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1320
• Professor: Kirill Zaynullin

Document Summary

Mat1320e calculus i: how derivatives shape graphs and l"hospital"s rule ( nov. 28) Critical numbers and how to nd them. Extreme value theorem local maximum local minimum. ) existence of absolute extrema of a continuous function on a closed interval. Using the first derivative: critical numbers, intervals of. Derivatives and graphs: remember: the derivative is a function that tells us about the slopes of tangents, let y = f (x). X f 0(x) = 0 () f ( x ) has a horizontal tangent at x f 0(x) < 0 () f cx) is decreasing at. If f 0(x) > 0, then the function is increasing on that interval. If f 0(x) < 0, then the function is decreasing on that interval: if the intervals to the left and right of a critical number x = c switch. From decreasing to increasing, respectively, then f has a local minimum at x = c, at coordinates (c, f (c)).