00:01
In this problem we are given the surface x square minus 4y square plus z square plus y z is equal to 8 and the point 3, 2, negative 5.
00:17
The first question is to determine the equation of the tangent plane to the surface at the given point.
00:24
Now consider the surface of the form x, y z is equal to some constant k.
00:31
Then the tangent plane to the surface at the point x, y, not, y, not, is said not can be determined as fx at the point x -not y -not -s -0 times x -minus -0, plus f -y -at -the -point x -0 -1 -0 times y -minus -0, plus f -s -sat -a -t at the point x -0 -0 -s0 times y -minus -0, y -0, plus f -s at the point x -0 -0 -0 -0, set -0 times is said -1.
01:03
Not is equal to 0 where fx, fy and f -zad are the partial derivatives of the function f of xy -sad and this is the required equation of the tangent plane.
01:14
So here for the surface we have f of xy -sad is equal to x -square minus 4 y square plus z -square plus y -sad and the point take it as the point p to be 3 -2 negative 5.
01:32
Now find the partial derivative of f with respect to x and it is 2x and fx at the point p is 2 times 3 which is 6.
01:45
Similarly, find the partial derivative of f with respect to y and it is negative 8y plus z and the partial derivative at the point p is negative 8 times 2 minus 5 which is negative 21...