Question

On the interval (0,4pi), the function, f(x)=cosx-x becomes f"(x)=cosx. Possible inflection points would include x=pi/2, x=3pi/2, x=5pi/2, and x=7pi/2. How do I find "true" points of inflection? Like using the second derivative test.

Answer 1

f''=cos x =0
x= pi/2 , 3pi/2 , 5pi/2 , 7pi/2