Abstract: A central problem in curve theory is to describe the extrinsic geometry of a curve C in P^r with fixed genus and degree. The Maximal Rank Conjecture predicts that for a general curve C in P^r, there should be "correct number" of independent hypersurfaces of degree k containing it. In this talk, I will describe the deformation theory of the space of quadrics containing C_t, as C_t moves in a one parameter family. For some special cases, we will show that even if C_0 has too many quardics containing it, we can deform to C_t such that C_t is contained in "correct number" of quadrics.