This assignment is based on  Maple worksheets  "Partial Derivatives and Tangent Planes" (tangent.mws)  and  "Gradients, Directional Derivatives and Rates of Change" (gradients.mws)

1.   Consider the function

(a)  Use Maple to find the tangent plane of this function at the point (-1, 1). .

(b)  Use Maple to plot the tangent plane and the graph of the function f(x,y) for x and y in [-7, 7]. Use different colors and styles for two surfaces.
 

2.   Consider the function

(a)  Use Maple to find the gradient at the point (0, 0) as well as the directional derivative in the direction of (1, 2).

(b)  Use Maple to plot the contour diagrams and the field of gradients of g(x,y)  for x and y in [-5, 5] on the same plot.
 
 

3.   Consider the function

(a)  Use Maple to find the gradient at the point (0, 1, 0) as well as the directional derivative in the direction of (1, 2, 1).

(b)  Use Maple to plot the level surfaces of the function F(x,y,z) for x and y in [-7, 7] along with thefield of gradients of  F(x,y,z).