Calculus Question

Question

Find any points of inflection for the function y = x-cosx on the interval [0,2pi].

Help!?

Answer 1

Find where y'' = 0, and make sure there is a change in the sign of y'' at opposite sides of the point, and it will be a point of inflection.

 

y = x - cosx

 

y' = 1 + sinx

 

y'' = cosx

 

cosx = 0 at π/2 and 3π/2

 

cosx > 0 between 0 and π/2

cosx < 0 between π/2 and 3π/2

cosx > 0 between 3π/2 and 2π

 

It looks like you have inflection points at π/2 and 3π/2.