The continuous function g, consisting of two line segments and a parabola, is defined on the...

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The continuous function g, consisting of two line segments and a parabola, is defined on the closed interval [-3, 6], is shown. Let f be a function such that f(1) = 10 n 9 8 7 6 5 4 3 2 1 0- -¹.3 5 Part A: Complete the table with positive, negative, or 0 to describe g' and g". Justify your answers. (3 points) -3 < x < -1 -1 <x<2 2<x<5 5<x<6 g(x) positive positive positive positive g'(x) g"(x) X Part B: Find the x-coordinate of any critical points of f and classify as a relative minimum, a relative maximum, or neither. Justify your answers. (3 points) Part C: Find all values of x at which the graph of f has a point of inflection. Justify your answers. (2 points) Part D: Let ʼn be the function defined by h(x) = 2f(x)g(x). Is h increasing or decreasing at x = 1? Justify your answer. (2 points) 1 and f'(x) = ex(1 - x). e The continuous function g, consisting of two line segments and a parabola, is defined on the closed interval [-3, 6], is shown. Let f be a function such that f(1) = 10 n 9 8 7 6 5 4 3 2 1 0- -¹.3 5 Part A: Complete the table with positive, negative, or 0 to describe g' and g". Justify your answers. (3 points) -3 < x < -1 -1 <x<2 2<x<5 5<x<6 g(x) positive positive positive positive g'(x) g"(x) X Part B: Find the x-coordinate of any critical points of f and classify as a relative minimum, a relative maximum, or neither. Justify your answers. (3 points) Part C: Find all values of x at which the graph of f has a point of inflection. Justify your answers. (2 points) Part D: Let ʼn be the function defined by h(x) = 2f(x)g(x). Is h increasing or decreasing at x = 1? Justify your answer. (2 points) 1 and f'(x) = ex(1 - x). e