What are the points of inflection of #f(x)=x+cosx # on the interval #x in [0,2pi]#?
A point of inflection is a point in which the function switches from being concave to convex, or vice versa. Our tool to verify if a function is concave or convex is the second derivative, more precisely its sign: if
So, look for the convex/concave switch is the same as looking for the positive/negative switch for the second derivative.
So, first of all, let's compute it: since the derivative of a sum is the sum of the derivatives, we have
And since we need to refer to the
The second derivative is