Practice: Optimization

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

intermediate

f_{xx} (a, b) = 4, f_{y y} (a, b) = 9, f_{x y} (a, b) = 6

at a critical point, the point is

Q2.

basic

Critical points of

f (x, y) = x^{2} + y^{2} - 2 x + 4 y + 5

are

Q3.

basic

Extreme Value Theorem requires the domain to be

Q4.

basic

D = f_{xx} f_{y y} - (f_{x y})^{2} < 0

at a critical point implies

Q5.

basic

At a local maximum of

f (x, y)

, what must be true?

Q6.

basic

The function

f (x, y) = x^{2} - y^{2}

has

Q7.

basic

On a closed bounded region, the absolute maximum of a continuous

f

can occur

Q8.

intermediate

If you parameterize the boundary

x^{2} + y^{2} = 4

with

x = 2 cos t, y = 2 sin t

, then

f (x, y)

on the boundary becomes