Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) f(x) = x + 5 cos x, [0, 2𝜋]. Describe the concavity. (Select all that apply.)

Answer 1

f'(x) = 1 - 5sinx; f''(x) = - 5cosx = 0; cosx = 0; x = π/2, 3π/2. At π/2 and 3π/2 f''(x) chenged sighn.

So, (π/2, π/2) and (3π/2, 3π/2) points of inflection