langrange interpolation and derivative enquiry

zonexo

hi,

i was reading a paper which uses one-dimensional Lagrange interpolation. Points A,B,D,E,C,P all lie along a line. Functional values at A,B,D,E are known. Dp/d(line)=0 at C. How can one use these info to get the value at P? I thought langrange interpolation only uses functional values. How do I make use of the dp/d(line)=0 at C?

Thank you