15/9/22, 15:25
Actividad 1 - Guía 4-Laura Cortes
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Student: Laura Cortes
Date: 09/15/22
Instructor: JOSE ALEXANDER
FUENTES MONTOYA
Course: Análisis Multivariado y Funcional
G1C3
Assignment: Actividad 1 - Guía 4
Find an equation for the plane that is tangent to the given surface at the given point.
z
= y − x (1,2,1)
The tangent plane at the point on the level surface of a differentiable function f is the plane through
normal to . The tangent plane to at is given by the following equation.
P0x0,y0,z0f(x,y,z) = c
P0
∇
f |P0f(x,y,z) = c P0
f + f + f = 0
xP0x − x0 y P0y − y0 z P0z − z0
Begin by setting the equation for the given surface equal to zero.
z = y − x
zy − x − = 0 Rewrite the equation.
Find .
∂
f
∂
x
f(x,y,z) = zy − x −
∂
f
∂
x=−1
2 y − x Differentiate.
Now find by substituting the values of the given point and simplifying.fxP0
∂
f
∂
x=−1
2 y − x
fxP0=−1
2 2 − 1 Substitute.
fxP0=−1
2Simplify.
Next find .
∂
f
∂
y
f(x,y,z) = zy − x −
∂
f
∂
y=1
2 y − x Differentiate.
Now find by substituting the values of the given point and simplifying.fyP0
