Is the following statement "Equation of the tangent plane to...

Is the following statement "Equation of the tangent plane to the surface [ e^{z y}+x z^{2}=6 x y^{4} z^{3} ] at the point ( (-1,0,1) ) is [ x+y-2 z=3 ] true or false? Select one: True False

Transcript

00:01 To find the equation of the tangent plane to this surface, let's first write the equation for this surface in the form f of x y z is equal to zero.

00:14 Okay so i'm just going to take this term and subtract it on both sides so we have f of x y z is equal to e to the z y power plus x z squared minus 6 x y to the fourth times z cubed.

00:32 Okay which is equal to zero.

00:35 Then the equation of the tangent plane to the surface at this point has the form partial derivative of f with respect to x evaluated at the point negative one zero one times x minus the x coordinate of the point which is negative one plus the partial derivative of f with respect to y evaluated at the point multiplied by y minus the y coordinate of the point which is zero plus the partial derivative with respect to z evaluated at the point multiplied by z minus the z coordinate of the point which is one.

01:14 Okay and this is equal to zero.

01:18 So let's solve this.

01:20 We have zero is equal to the partial derivative of f with respect to x is z squared minus 6 y to the fourth z cubed.

01:32 Okay so we need to evaluate this at the point negative one zero one.

01:39 Okay and then we're multiplying by x plus one.

01:43 Next we have the partial derivative with respect to y.

01:46 This is equal to z times e to the z y power minus six times four which is 24 x y cubed z cubed.

01:57 Okay again evaluated at the point multiplied by y and then we have the partial derivative with respect to z which is y times e to the z y power plus 2 x z minus three times six which is 18 x y to the fourth z squared evaluated at the point multiplied by z minus one.

02:32 Okay so we have zero is equal to let's plug in the values of the point into this partial derivative...

Question

Is the following statement "Equation of the tangent plane to the surface [ e^{z y}+x z^{2}=6 x y^{4} z^{3} ] at the point ( (-1,0,1) ) is [ x+y-2 z=3 ] true or false? Select one: True False

Please give Ace some feedback