Given the function g(x) = 6x³ +54x² + 90x, find the first

Last updated: 7/20/2022

Given the function g(x) = 6x³ +54x² + 90x, find the first derivative, g'(x). g'(x) = Notice that g'(x) 0 when a = 5, that is, g'(-5) = 0. 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. Find the second derivative, g''(x). g''(x) = Evaluate g''(-5). g''(-5) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = -5? At x = -5 the graph of g(x) is 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? At x = - 5 there is a local