Question

Find an equation of the tangent plane to the surface z=ln(x-6y) at the point(7,1,0)

Answer 1

The tangent plane equation of tangent plane is

z = x - 6y -1

This is further explained below.

What is the equation of the tangent plane to the surface z=ln(x-6y) at the point(7,1,0)?

Generally, Given surface is z = ln(x − 6y) ,

Given point is $(x_0, y_0 , z_0)$ = (7, 1, 0)

partially differentiating with respect to x

== >zx = [1/(x - 6y)] (1) = 1/(x - 6y)

zx (7 , 1 , 0) = 1/(7 - 6(1)) = 1

Partially differentiating with respect to y

zy = [1/(x - 6y)] (-6)

zy = -6/(x - 6y)

zy(7 , 1 , 0) = -6/(7 - 6(1)) = -6

Equation of tangent plane is z - $z_0$ = zx(x -$x_0$) + zy(y - $y_0$)

z - 0 = 1(x - 7) + (-6)(y - 1)

z = x - 7 -6y + 6

z = x - 6y -1

In conclusion, equation of tangent plane is z = x - 6y -1

Read more about the tangent plane

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