Find a second-degree polynomial P such that P(1) = 2, P'(1) = 5, and P''(1) = 8.

Question

 I am supposed to find a second degree polynomial, but I don't understand where I am supposed to start.

Answer 1

P(x) = Ax² + Bx + C

 

P'(x) = 2Ax + B

 

P"(x) = 2A

 

Since P"(1) = 8, 2A = 8.  So, A = 4.

 

P'(1) = 2A + B = 8 + B = 5

 

                               B = -3

 

P(1) = A + B + C = 2

 

          4 - 3 + C = 2

 

                     C = 1

 

P(x) = 4x² - 3x + 1`