Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that g'(æ) = 0 when z = 4, that is, g'(4) = 0. Now, we want to know whether there is a local minimum or local maximum at æ = 4, so we will use the second derivative test. Find the second derivative, g''(x). = (2),,6 Evaluate g''(4). g'"(4) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at æ = 4? At a = 4 the graph of g(x) is Select an answer e Based on the concavity of g(x) at æ = 4, does this mean that there is a local minimum or local maximum at x = 4? At æ = 4 there is a local Select an answer e

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