00:01
Let's find an equation of the tangent plane to the surface z equals x sign of x plus y at the given point.
00:11
So let's recall the formula for the tangent plane where the surface is given by f.
00:25
So here we're just adopting the same convention as the book where z is f of x y unless stated otherwise.
00:37
So using this, the equation of the plane of the tangent plane.
00:46
And here what i mean by x not y0 and z not it's in general the point at which the plane is tangent to the surface so in this case these values are given negative 1 1 and 0 then we multiply that by x minus x not and similarly for the partial derivative with respect to y multiply by y minus y not so we can see based on the formula we'll need those partial derivatives so let's go ahead and evaluate those, differentiate with respect to x, we see x appears in both factors, so we'll go ahead and use the product rule.
01:39
And then from this, you can go ahead and plug in x not and y not.
01:43
These are given.
01:48
So we'll have sine of zero, minus one, and then cosine of zero.
01:55
So sign of zero is zero, cosine of zero is one...