Find All the Local Maxima, Local Minima, and Saddle Points

question 132

Multiple Choice

Find all the local maxima, local minima, and saddle points of the function.
-f(x, y) = 10xy(x + y) + 4

• A) f(10, 0) = 4, local minimum; f(0, 10) = 4, local minimum
• B) f(0, 0) = 4, test is inconclusive
• C) f(10, 10) = 20,004, local maximum
• D) f(0, 0) = 4, saddle point; f(10, 10) = 20,004, local maximum

---

Definitions:

Skull

The bony structure forming the head, housing the brain and providing protection to it.

Spongy Bones

A type of bone tissue characterized by a porous, honeycomb-like structure, found primarily at the ends of long bones and in the interior of vertebrae, playing a key role in movement and support.

Endosteum

A membrane that lines the medullary cavity and the holes of spongy bone.

Occipital Bone

A cranial bone located at the back and lower part of the skull, playing a key role in protecting the brain and supporting the head.