IB Mathematics SL – Derivatives, Points of inflexion
We know that
and the second derivative function changes sign around
the function has a point of inflection.
The first derivative function is
The second derivative function is
By setting the second derivative equal to zero,
To determine the set of values for which the function is concave up or concave down we need to solve the following inequality
We observe that the function is concave up when
and is concave down when
the function has a point of inflexion which has coordinates (0,2).
Hope these help!!