4.22 On using the sign tests

(i) To find local maxima and minima, look for stationary points by solving $f^{\prime}(a)=0,$ then determine their nature.

(ii) The sign tests of Theorem 4.16 describe the local behaviour of the function; asymptotes can describe the shape for large $x$ and $y$. A local minimum may not be the smallest value taken by the function overall.