00:01
Okay, we've been asked to find the tangent plane to this function at the point negative 1 -2.
00:06
First of all, notice that f of x, y is equal to z, right? and that f of negative 1 -2 is equal to 2 minus 4 times 4, negative 16, so plus 16, which is 18.
00:31
Okay, so this is the point negative 1 to 18.
00:38
Okay, so we're going to rewrite our function as a level curve of a function of three variables.
00:46
So this is f of x, y, minus z, which is 2x squared minus 4 x, x, y, minus z.
01:02
Okay, so now we'll find the gradient of this function.
01:06
So the gradient of capital f of x, y, z is equal to the partial with respect to x is 4x minus 4 y squared.
01:20
The partial with respect to y is minus 8xy and the partial with respect to z is negative one.
01:31
Okay, so we need to evaluate the gradient at our point, which is negative 1, 2, 18...