Answer:
Rate of change of function in the direction of normal to the given surface at ( 3 , 4 , 3 ) is
Step-by-step explanation:
Given:
Function, f( x , y , z ) = xyz
Equation of surface, yx² + xy² + yz² = 120
To find: Rate of change of function in the direction of normal to the given surface at ( 3 , 4 , 3 )
The Gradient of the normal to the surface
Gradient at ( 3 , 4 , 3 )
The Change in the directional derivative of f in given direction is,
Therefore, Rate of change of function in the direction of normal to the given surface at ( 3 , 4 , 3 ) is