Problem 1. Read sections 10.3 and 10.4
Problem 2. Find the equation of the plane tangent to the graph of
at the point .
Problem 3. For this problem we will use the function from Problem 2.
(a) Compute the derivative matrix .
(b) Compute the linear approximation for at the point .
Problem 4. Given the function , compute the derivative matrix .
Problem 5. (a) Given a function , explain why its derivative matrix is a “row matrix.”
(b) If instead of arranging the partials of in a matrix we arrange them in a vector, then we do not call the resulting vector expression a “matrix.” Instead we call it the gradient of and we notate it as
Compute the derivative matrix and compute the gradient, , of the function .
(c ) Find al points where .
(d) What do the points in part (c) have to do with the graph of ?