Final answer:
The network of fibrous proteins supporting the plasma membrane is known as the cytoskeleton, which includes the actin cortex and is responsible for maintaining cell shape and integrity.
Step-by-step explanation:
The extensive support network of fibrous proteins that reinforces the fragile plasma membrane is called the cytoskeleton. This network is made up of microfilaments, intermediate filaments, and microtubules. These components not only maintain cell shape but also secure organelles in place, aid in intracellular movement, and allow for cellular motion within multicellular organisms.
Under the plasma membrane lies the actin cortex, which is a layer of crosslinked actin filaments that contribute to the cell's mechanical properties and its ability to withstand deformations. The actin cortex is a critical aspect of the cytoskeleton's function in supporting the plasma membrane.
Thus, the correct answer to the student's question is (c) cytoskeleton.