00:01
So we are given the function f of x comma y is equals to 7 plus x y minus of x minus of 2 y where d is the closed triangle region whose vertices we have been given 1 comma 0, 5 comma 0 and 1 comma 4.
00:20
So you have to find the absolute maximum and absolute minimum values.
00:25
So to find the absolute maximum minimum first of all we need to find the derivative of the given function with respect to s that is f of x.
00:32
So this will comes out equals to.
00:35
So we are differentiating with respect to x that means y will be treated as constant and hence this whole term, okay this term and this term, this term sorry is going to be 0 and only these two terms will going to give me the required derivative.
00:53
So how it would be? the y will be common derivative of x is going to be 1 minus derivative of x is going to be 1.
01:00
Similarly f of y this will be goes to x minus of 2 equating both is to 0 that is f of x to 0 and f of y to 0.
01:11
We get the required equation as y is equals to 1 and x is equals to 2.
01:16
So basically these are nothing but what? the critical points.
01:19
So here we will say the critical point are 2 comma 1.
01:26
So by using this the equation of lines bounding the region can be form like y is equals to 1 y sorry x is equals to 1 y equals to 0...