Find the rate of change of f(x, y,z)=xyzf(x, y,z)=xyz in the direction normal to the surface yx2+xy2+yz2=120yx2+xy2+yz2=120 at (3,4,3)(3,4,3). (use symbolic notation and fractions where needed.) rate of change =

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

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!