MediumCalculusca-035

Critical Points of a Cubic

Problem

Find all real critical points of the cubic f(x) = a*x^3 + b*x^2 + c*x + d by solving f'(x) = 3*a*x^2 + 2*b*x + c = 0.

Return the distinct real roots sorted in ascending order (an empty list if there are none). The constant d does not affect the result.

Hint

Solve the quadratic f'(x) = 0 with the discriminant and keep only real roots.

case 1

in: [1,0,-3,0]

expected: [-1,1]

case 2

in: [1,-3,2,0]

expected: [0.42264973081037427,1.5773502691896257]

case 3

in: [0,1,-4,5]

expected: [2]

case 4

in: [1,0,1,0]

expected: []

case 5

in: [1,0,0,0]

expected: [0]

Starter codePython

def critical_points(a, b, c, d):
    # Return a sorted list of critical x values
    # Your code here
    pass

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