00:01
In this question, we are told that f is a differentiable function, and we are given the values of f and its first derivatives at the point 4 -negative 7.
00:09
And we are asked to find the values of the, approximate the values of the function f at several points.
00:18
And to do that, we will use the tangent, the linear approximation, or the tangent also called the tangent plane approximation.
00:27
It says that f of x y approximately equals to l of x.
00:35
Where l of xy equals to f of 4 negative 7 plus f x of 4 negative 7 times x minus 4 plus f y of 4 negative 7 times y plus 7 what we are going to do next is we'll just replace f x and f y by their numbers by their values f is negative 4, fx equals to 3, and fy equals to 2.
01:22
So we are going to get that l of xy equals to negative 4 plus 3 times x minus 4 plus 2 times y plus 7.
01:38
And we will use that formula to approximate the number, the values of the function...