In 2 -1/x dx

The continuous function f is defined for −4 ≤ x ≤ 4. The graph of f, shown above, consists of two line segments and portions of three parabolas. The graph has horizontal tangents at x=−1/2, x=1/2, and x=5/2. It is known that f(x)=−x^2 + 5x - 4 for 1≤x≤4. The areas of regions A and B bounded by the graph of ff and the x-axis are 3 and 5, respectively. Let g be the function defined by g(x)= (-4 to x) ∫f(t)ⅆt (a) Find g(0) and g(4). b)Find the absolute minimum value of g on the closed interval [−4,4]. Justify your answer. c) Find all intervals on which the graph of g is concave down. Give a reason for your answer.