EasyCalculusca-007

Second Derivative Central Difference

Problem

Approximate the second derivative of f(x) = sum(coeffs[i] * x^i) at x with the central difference formula:

f''(x) ≈ (f(x + h) - 2 * f(x) + f(x - h)) / h^2

Use the default step h = 1e-3.

Hint

The numerator is a centered second difference; divide it by h squared.

case 1

in: [[1,0,1],4]

expected: 2

case 2

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

expected: 12

case 3

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

expected: 0

case 4

in: [[5],3]

expected: 0

Starter codePython

def second_derivative(coeffs, x, h=1e-3):
    # coeffs[i] is the coefficient of x^i
    # Your code here
    pass

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