. Question 10 The function f(a) = 1 + 4x + 64x has one local minimum and one local maximum. This function has a local maximum at * = with value and a local minimum at * = with value Submit Question. Question 11 Given the function g(x) = 4x + 6x - 72x, find the first derivative, g' (x). g' (x) = Notice that g'(x) = 0 when x = - 3, that is, g'( - 3) = 0. Now, we want to know whether there is a local minimum or local maximum at x = - 3, so we will use the second derivative test. Find the second derivative, g' ' (x). g"(x) = Evaluate g' '( - 3). g"( - 3) = Based on the sign of this number, does this mean the graph of g( ) is concave up or concave down at c = - . concave up At x = - 3 the graph of g(a) is Select an answer . concave down ? Based on the concavity of g() at x = - 3, does this mean that there is a local minimum or local maximum at * = - 3? . minimum 7 At * = - 3 there is a local Select an answer v maximum Question Help: Video Submit Question. Question 12 Given the function g(x) = 8x + 36x - 96x, find the first derivative, g' (x). g'(x) = Notice that g' (x) = 0 when x = 1, that is, g'(1) = 0. Now, we want to know whether there is a local minimum or local maximum at a = 1, so we will use the second derivative test. Find the second derivative, g' ' (x). g"(x) = Evaluate g' ' (1). g"(1) = Based on the sign of this number, does this mean the graph of g( ) is concave up or concave down at x = 1? . concave up At a = 1 the graph of g(a ) is Select an answer v concave down Based on the concavity of g(x ) at x = 1, does this mean that there is a local minimum or local maximum at x = 1? . Maximum At * = 1 there is a local Select an answerv minimum Question Help: Video Submit