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 1x4. 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)t

(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.

needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers a for which f (x) is a real number. 00 7+ (-2, 3) 4+ 3 B 2- - X -4 - 3 -2 -1 2 3 A -2 Graph of f The continuous function f is defined for -4 = 5, and x = . It is known that f (x) = -x2 +5x - 4 for 1