Question

Find the equation of the tangent plane at P = (0,3,-1) to the surface with equation 2e^x + e^(z+1) = xy + y - 3

Answer 1

In general, how would you find the tangent plane at a given point? What is required?

Answer 2

Fx and Fy and F

Answer 3

Okie dokie, first we need to transform the equation to look like

f(x,y,z) = 0

and then recall that the general equation of a tangent plane at a given point on a surface is given by

\[f_x(x_0,y_0,z_0)(x-x_0)+f_y(x_0,y_0,z_0)(y-y_0)+f_z(x_0,y_0,z_0)(z-z_0)=0\]

Here f_x, f_y, f_z, e.t.c stand for your partial derivatives with respect to x, y, z and (x_0,y_0,z_0) is your initial point.

There is an easy form of this equation if you reduce the initial equation into the form z=f(x,y).

Answer 4

Wanna get me started

Answer 5

We'll go step by step, make your above equation = 0. Write it out on here for everyone to see so that we're on the same page : )