What is the rate of change of this function at the point

Question

1. Consider the function f(x,y,z) = x² + (3y/z).

What is the rate of change of this function at the point (3,2,4) in the direction towards (1,4,3)?

What is the greatest rate of change of this function at the point (3,2,4)?

Find the equation of the plane tangent to x² + (3y/z) = 7 at the point(2,1,1).

2. Use the tangent plane approximation of f(x, y) = y√(1 +x³) at the point (2, 1) to approximate the value of f(2.2, 1.3).