Given the function 9(3) 2 83:3 + 84:2 + 2882:, nd the rst derivative, {(3). W) = :l Notice thatg'(:1:) : II] when 2: = 4, that is, g'[ 4] = 0. Now, we want to know whether there is a local minimum or local maximum at I = 4, so we will use the second derivative test. Find the second derivative, 9' '(I). W) =:] Evaluate g'( 4). 9' w 4) = :] Based on the sign of this number, does this mean the graph of g(:l:] is concave us or ooncave down at 2: = 4? [Answer either up or down -- watch your spelling!!] At 2 = 4 the graph of 9(3) is concave Based on the concavity of 9(2) at 2 = 4, does this mean that there is a local minimum or local maximum at 2 = 4? [Answer either minimum or maximum watch your spelling!!] At a: = 4 there is a local