Unless otherwise specified, the domain of a function, , is assumed to be the set of all real numbers for which () is a real number. Let be a twice-differentiable function such that ′ () = 0. . The second derivative of is given by "() = 2 cos ( 2 + ) for −1 ≤ ≤ 3. (a) On what open intervals contained in −1 < < 3 is the graph of concave up? Give a reason for your answer (b) Does have a relative minimum, a relative maximum, or neither at = 1 ? Justify your answer.
(c) Does the graph of have a point of inflection at = 0? Give a reason for your answer.