determine the open intervals

Question

Determine the open intervals on which the graph is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

y = 5x + (7/sin x), (−π, π)

concave upward _____

concave downward_____

Answer 1

y = 5x + (7/sin x), (−π, π)

y' = 5 - 7Cos(x) / Sin²x = 5 - 7/Cot(x)/Sin(x)

concave upward _(0,π)___

concave downward_(-π,0)__