Find the Absolute Maxima and Minima of the Function on the Given

question 248

Multiple Choice

Find the absolute maxima and minima of the function on the given domain.
- $$f ( x , y ) = 8 x ^ { 2 } + 9 y ^ { 2 } \text { on the closed triangular region bounded by the lines } y = x , y = 2 x \text {, and } x + y = 6$$

• A) Absolute maximum: 153 at (3, 3); absolute minimum: 0 at (0, 0)
• B) Absolute maximum: 153 at (3, 3); absolute minimum: 68 at (2, 2)
• C) Absolute maximum: 176 at (2, 4); absolute minimum: 0 at (0, 0)
• D) Absolute maximum: 176 at (2, 4); absolute minimum: 153 at (3, 3)

---

Definitions:

Subduction Zone

A tectonic plate boundary where one plate moves under another and is forced into the mantle, typically creating earthquakes and volcanic activity.

Earthquake Risk

Earthquake risk refers to the probability of earthquakes occurring in a region and the potential damage they can cause to life, property, and the environment.

Modified Mercalli Intensity

A scale for measuring the intensity of an earthquake based on its observed effects on people, buildings, and the Earth's surface.

Richter Magnitude

The Richter magnitude scale is a numeric scale used to express the energy released by an earthquake, with each whole number representing a tenfold increase in measured amplitude.