Errors and Approximations
If is a function of , then the error in is
However, this is an approximation.
Note: If necessary, we take log on both sides.
Maxima and Minima (Functions of Several Variables)
We have studied the process of finding extreme values of . Now, we will see the same for .
First, we equate and to . We get those pairs , which can either be maxima, minima or saddle points.
We then find , and for these pairs.
I) , – Gives maximum value
II) , – Gives minimum value
III) – Saddle point
IV) – No conclusion possible
Lagrange’s Method of Undetermined Multipliers
This method is used when the maximum and minimum of a function are to be obtained under certain constraints (like the optimization problems). We form a linear relation between the function and the constraint using a Lagrange multiplier and differentiate it partially w.r.t. the variables. We then eliminate the variables and parameter and get an equation. The roots of that equation are the extreme values.