MATH-M 119 Study Guide - Fall 2018, Comprehensive Midterm Notes - Microsoft Powerpoint, Graph Of A Function, Tangent

• School: IU
• Department: Mathematics
• Course: MATH-M 119
• Professor: Tracy Whelan

Document Summary

Math-m119 lecture 12 interpretations of derivatives. If (cid:4666)(cid:1876)(cid:4667)> (cid:882) on interval (x1, x2), f(x) increases on the interval. If (cid:4666)(cid:1876)(cid:4667)< (cid:882) on interval (x1, x2), f(x) decreases on the interval. If (cid:4666)(cid:1876)(cid:4667)> (cid:882) on interval (x1, x2), f"(x) increases on the interval, so f is concave up on the. If (cid:4666)(cid:1876)(cid:4667)< (cid:882) on interval (x1, x2), f"(x) decreases on the interval, so f is concave down on the. To describe the second derivative (f""), have to first describe first derivative (f"): F"" is the first derivative of f" interval interval. From a graph of f, we can determine the sign of f, f", and f"" at a given point: For f(x), positive if the curve is above the x-axis and negative if below the x-axis. For f"(x), positive if the curve is increasing and negative if decreasing. For f""(x), positive if the curve is concave up and negative in concave down. Velocity is the derivative of the position function.