Module 13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 38 : Second derivative test for local maxima / minima & saddle points [Section 38.1]
(4)
Let
Find all the critical points of and analyze them for being points of local maximum/minimum/saddle point. Every point along -axis and -axis is a point of local minimum.
(5)
Let
Show that has only two critical points, both being points of local maximum. (Note that for a function of a single variable, between any two points of local maximum, there must be a point of local minimum).
and analyze them for being points of local maximum/minimum/saddle point. Every point along 
-axis and 
-axis is a point of local minimum. 
has only two critical points, both being points of local maximum. (Note that for a function of a single variable, between any two points of local maximum, there must be a point of local minimum). 
