Step 1: Definition of auxotrophy.
An auxotroph is a mutant organism that cannot synthesize a particular organic compound required for its growth. It must obtain that compound from the environment.
Step 2: Compare with other types.
(A) Heterotrophs obtain carbon from organic sources but may still synthesize essential nutrients.
(B) Chemotrophs gain energy from chemical compounds.
(C) Autotrophs synthesize organic compounds from CO$_2$.
Step 3: Conclusion.
Only auxotrophs fail to grow without the required nutrient, such as an amino acid or vitamin.