00:01
We have been given x square minus 4 y square plus z square plus y z is equals to 17.
00:09
So, that means we have f x comma y comma z is equals to x square minus 4 y square plus z square plus y z minus 17.
00:21
So, now let us partially differentiate this equation over here with respect to x y and z.
00:25
So, we will have del f upon del x now this would be equals to what.
00:29
So, in this case scenario i will be taking this function over here and your variable y and z would be treated as constant.
00:35
So, when you will differentiate this, this would be 2 x over here.
00:38
Now, again let us differentiate the same function with respect to y.
00:41
So, you will have del f upon del y is equals to what you will get from here minus 8 y plus over here you will get what this would be z over here.
00:50
Remember this case scenario your x and z were the constant.
00:53
Now, again let us partial differentiate with respect to z.
00:56
So, this would be del f upon del z is equals to what.
01:00
So, from here you will get 2 z plus y in this case scenario x and y were your constant.
01:06
Now, let us find the values of f x 5 comma 3 comma minus 7 because we have been given this point.
01:14
So, therefore, this would be equals to what.
01:15
So, your f x was what del f upon del x that means this value.
01:19
So, this would be 2 multiplied by you only have 5 over here.
01:22
So, this would be 5 and this would be equals to what this would be equals to 10.
01:26
Now, why did i say we have 5 over here because we just have x in this situation and over here we are taking 5...