CSC 349A Nunlerical Analysis: I A01, A02 7 6. Consider the following piecewise cubic polynomial S[:r} 30:2x133= [lg-3:31 _ 81=a+b(-:c1)+c(11)2+d[:r1)3, 13mg? (a) [8 points] Determine the values of a, 45: c5 and of. so that 3(3) is a natural cubic spline. (b) [2 points] Determine the values of a, b, c5 and C! so that 3(1):} is a clamped cubic spline with S'(2] = 2. You do not need to recalculate any values that are the same from part (a)