please answer all questions in detail.

Question 4: (Geometry of space curves)-(18 points (a): Let c(t) = (t, t2, +3). Find: . the Frenet frame { B, N, T}. . k(t) and k(0). . T(t) and T(0). (b): Given that k(t) = c (t)xc"(t)| |c' (t) |3 1, show that for the plane curve y = f(x), k(x) = - If" (20 ) | [1+(f'(x)) 212 (c): Let y = f(x) = x2. . find k(x) . Plot f(x) and k(x) on the same graph. . Can you relate the two graphs? That is, can you explain the behaviour of the second graph in relation to the first graph