Observe that f ′(x) ≥ 0, for all x ∈ R and in particular
f ′(x) > 0, for values close to 1 and to the left and to the right of 1 Therefore, by first
derivative test, the point x = 1 is neither a point of local maxima nor a point of local
minima Hence x = 1 is a point of inflexion Remark One may note that since f ′(x), in Example 30, never changes its sign on R,
graph of f has no turning points and hence no point of local maxima or local minima