11.4  Tangent Planes and Linear Approximations

Zooming in on a tangent plane

objectives

• to be able to find the equation of the tangent plane to a surface
• to be able to demonstrate that a function f(x,y) is differentiable at a point
• to be able to find the linearization of f(x,y) at a point
• to be able to find the equation of the tangent plane to a surface described by parametric equations
• to be able to find the total differential of a function

• tangent planes

 
• equation of a tangent plane

 
• linear approximations

 
• differentiable function f(x,y)

 
• differentials

 
• total differentials

 

• finding an equation to the tangent plane, #1  (zoom in)

 

 
 
 
 
 
 
 
 
 
 
 
 

• determining if a function is differentiable,
• finding the linearization of the function at a point, #10

 

 
 
 
 
 
 
 
 
 
 
 
 

• finding the total differential of a function, #19

 

 
 
 
 
 
 
 
 
 
 
 
 
 

• understanding differentials, #24

 

 
 
 
 
 
 
 
 
 
 
 
 
 

• applying differentials, #26

 

 
 
 
 
 
 
 
 
 
 
 
 
 

• finding equation of tangent plane to a parametric surface, #33