Second-Order Taylor Approximation

Problem

The second-order Taylor approximation of f about the point a is T(x) = f(a) + f'(a) * (x - a) + 0.5 * f''(a) * (x - a)^2.

Given a polynomial by its coefficient list (index i holds the coefficient of x^i), the expansion point a, and the evaluation point x, return T(x).

Hint

For a quadratic polynomial the second-order approximation is exact.

case 1

in: [[0,0,1],1,2]

expected: 4

case 2

in: [[1,1,1],0,1]

expected: 3

case 3

in: [[0,0,0,1],1,1.1]

expected: 1.3300000000000003

case 4

in: [[2],0,5]

expected: 2

Starter codePython

def second_order_taylor(coeffs, a, x):
    # Your code here
    pass

4 test cases · run your code against them in the editor