Problem 7.1. Let f (x, y) = x4 ? 3xy + 2y2.
(a) Compute the partial derivatives of f as well as itsdiscriminant. Then use
solve to find the critical points and to classify each one as alocal maximum,
local minimum, or saddle point.
(b) Check your answer to (a) by showing that fminsearch correctlylocates
the same local minima when you start at (0.5, 0.5) or at (?0.5,0.5).
(c) What happens when you apply fminsearch with a starting valueof
(0, 0)? Explain your answer.
(d) What are the values of f at the extrema? Now, using fmesh,graph the function
on a rectangle that includes all the critical points. Experimentwith view
and axis until you get a picture that shows the behavior near thecritical points.
Use the graph and all the previous data to justify the assertion:Sometimes symbolic
and/or numerical computations are more revealing than graphicalinformation.
