MATH 102 Lecture Notes - Lecture 14: Cell Division, Maxima And Minima

• School: UBC
• Department: Mathematics
• Course: MATH 102
• Professor: Elyse Yeager

Document Summary

Example 1: identify the extrema from the following graphs (yeager, ch. 6 slide 17) A: local minimum at x = 0 (because sign changes from (-) to (+) ) B: local maximum at x = 0 (because sign changes from (+) to (-) ) D: one local minimum and one local maximum (becasue sign changes from (-) to (+) to (-) ) Example 2: f (x) = x 4 2x3 + Step 1: derive f(x) to its rst derivative = 0 to nd the critical points. Therefore, it shows x = 0 is a local minimum, while x = 3 is still inconclusive. When x < 3, let x = 1. When x > 3, let x = 4. They are both positive values, so there is no sign change for f"(x) when x is greater and less than 3, so x = 3 is neither local minima or local maxima.