5. Let g be the function given by g(x) =x4 - 4x3 + 6x - 4x+...

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5. Let g be the function given by g(x) =x4 - 4x3 + 6x - 4x+ k, where k is a constant. A. On what intervals is g increasing? Justify your answer. g'(x) >0 for increasing function g(x) 4x-12x+12x-4 >0 4(x-3x+3x)(-1) >0 4(x-1) >0 (X-1) >0 X>1 g(x) is increasing on (1,00) B. On what intervals is g concave upward? Justify your answer. g(x) =12x-24x +12 = 12(x-2x+1) = 12 (X-1)2 g(x) >0 12(x-1)>0 (x-1) > 0 X-1>0 x-140 X >1 X <1 g(x) is concave upward on [(-0,1) U (1,00)] Calculus AB Assignment Applications of the Derivative C. Find the value of k for which g has 5 as its relative minimum. Justify your answer. 5. Let g be the function given by g(x) =x4 - 4x3 + 6x - 4x+ k, where k is a constant. A. On what intervals is g increasing? Justify your answer. g'(x) >0 for increasing function g(x) 4x-12x+12x-4 >0 4(x-3x+3x)(-1) >0 4(x-1) >0 (X-1) >0 X>1 g(x) is increasing on (1,00) B. On what intervals is g concave upward? Justify your answer. g(x) =12x-24x +12 = 12(x-2x+1) = 12 (X-1)2 g(x) >0 12(x-1)>0 (x-1) > 0 X-1>0 x-140 X >1 X <1 g(x) is concave upward on [(-0,1) U (1,00)] Calculus AB Assignment Applications of the Derivative C. Find the value of k for which g has 5 as its relative minimum. Justify your answer.

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5 A 9n x 3 244x6x4xk k in constant 9 3 9m x 4x3 6729xx 4x12x... View the full answer