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:

Muscle Fiber

The cylindrical, multinucleate cells that make up skeletal muscles, responsible for contracting to produce movement.

Myofibril

Within a muscle fiber, a threadlike array of proteins organized as a series of sarcomeres (contractile units).

Sarcomere

Contractile unit of muscle; an array of actin and myosin filaments arranged in parallel and bounded on either end by an array of cytoskeletal elements (a Z line).

Red Muscle Fibers

Muscle fibers with high myoglobin content and mitochondria, adapted for endurance and sustained activity by aerobic respiration.