Given the function g x 4x 18x g x Notice that g x 0 when x

Last updated: 4/18/2023

Given the function g x 4x 18x g x Notice that g x 0 when x Find the second derivative g x g x Evaluate g 5 g 5 Now we want to know whether there is a local minimum or local maximum at x 5 so we will use the second derivative test At x 5 the graph of g x is O concave down concave up 120x find the first derivative g x At x 5 there is a local O minimum maximum 5 That is g 5 0 Based on the sign of this number does this mean the graph of g x is concave up or concave down at x 5 Based on the concavity of g x at x 5 does this mean that there is a local minimum or local maximum at x 5