Given the functiOn g(x) = 6x3 + 9:32 36:13, find the first derivative, g'(:c). 91$) = i ' Notice thatg'(a:) = 0 when a: = 1, that is, g'(1) = 0. Now, we want to know whether there is a local minimum or local maximum at :L' = 1, so we will use the second derivative test. Find the second derivative, 9' ' (2:). 9"(93) =i ' Evaluate 9"(1). 9"(1) = \\ Based on the sign of this number, does this mean the graph of g(:c) is concave up or concave down at m = 1? At :1: = 1 the graph of g(:r:) is l Select an answer vi Based on the concavity of g(w) at a: = 1, does this mean that there is a local minimum or local maximum at :c = 1? At m = 1 there is a local Question Help: El Video Submit Question Given the function g(m) = 4:113 362:2 + 6011:, find the first derivative, g'(m). g'lm) = l l Notice thatg'($) = 0 when w = 5, that is, g'(5) = 0. Now, we want to know whether there is a local minimum or local maximum at :c = 5, so we will use the second derivative test. Find the second derivative, 9' '(w). 9"(m) = l ' Evaluate g"(5). 9' '(5) =i l Based on the sign of this number, does this mean the graph of g(:n) is concave up or concave down at :c = 5? At :5 = 5 the graph of g(sc) is | Select an answer v i Based on the concavity of g(:1:) at a: = 5, does this mean that there is a local minimum or local maximum at a: = 5? At :1: = 5 there is a local l Select an answer v| Question Help: El Video Submit