Given the function g(z) : 8m3 7 108$2 + 480m, find the first derivative, g'(m) W) =: Notice that g'(m) = 0 when x = 5, that is, g'(5) z 0. Now, we want to know whether there is a local minimum or local maximum at ac : 5, so we will use the second derivative test. Find the second derivative, g"(m). W: Evaluate g"(5). 3"(5) =i Based on the sign of this number, does this mean the graph of g(m) is concave up or concave down at m : 5? [Answer either up or down -- watch your spelling!!] At a: : 5 the graph of g(m) is concave' ' Based on the concavity of 31(1) at a: : 5, does this mean that there is a local minimum or local maximum at a: : 5? [Answer either minimum or maximum -- watch your spelling!!] At (c 2 5 there is a local