Verified answer

f'(x) = 1 -9sin(x)

f''(x) = -9cos(x)

f''(x) changes sign when cos(x) does and that is at x=pi/2 and 3pi/2

Since f(x) is continuous everywhere so x=pi/2 and 3pi/2 are the

points of inflection. Concavity at pi/2 changes from -ve to +ve

and from +ve to -ve at 3pi/2