Maxima and Minima Problems

Critical points

The second derivative test

Absolute extrema on closed regions

Applications

For a differentiable function of two variables, local extrema occur only where which condition holds?

A saddle point of f(x, y) is a critical point which is what?

The second derivative test's discriminant D equals which expression?

A critical point with D positive is a local minimum when which further condition holds?

When the second derivative test's discriminant D equals zero at a critical point, what does the test conclude?

The paraboloid f = x^2 + y^2 has one critical point. As a number, how many? Answer with a number.

For the saddle x^2 - y^2, the discriminant D is negative. As a sign, what is it? Answer with the single character.

The matrix of second partials is named for which mathematician, surname only? Answer in lowercase.

The regression line's least squares fit minimizes the sum of squared errors, and its slope and intercept are found by which condition?

On a closed bounded region, the absolute extrema's candidates include interior critical points and the boundary's extrema, found by which methods? Answer with two words.