EasyCalculusca-051

Total Differential Estimate

Problem

For f(x, y) = a*x^2 + b*y^2 + c*x*y, estimate the change in f for a small step (dx, dy) with the total differential:

df ≈ f_x * dx + f_y * dy

where f_x = 2*a*x + c*y and f_y = 2*b*y + c*x. Evaluate the differential at (x, y).

Hint

The total differential is the dot product of the gradient with the displacement.

case 1

in: [1,1,0,1,1,0.1,0.2]

expected: 0.6000000000000001

case 2

in: [1,0,1,0,0,0.5,1]

expected: 0

case 3

in: [2,3,1,1,2,0.01,-0.02]

expected: -0.2

case 4

in: [0,0,0,3,4,1,1]

expected: 0

Starter codePython

def total_differential(a, b, c, x, y, dx, dy):
    # Your code here
    pass

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