Final answer:
The constants a, b, c, and d are determined by solving a system of equations obtained by comparing the Gauss quadrature formula to the exact integral of a cubic polynomial. The response doesn't provide the constant d due to lack of relevant data.
Step-by-step explanation:
The question asks to find constants a, b, c, and d that make up a Gauss quadrature formula with a precision of degree 3. To do this, we need to find these constants such that the formula:
∫₋₁¹ f(x) dx = a f(-1) + b f(1) + c f'(-1) + d f'(1)
can accurately approximate the integral of any polynomial of degree 3 or lower. Since this involves a linear combination of the function and its derivatives evaluated at the endpoints of the interval [-1, 1], we equate the coefficients of the Gauss quadrature formula to the coefficients from the exact integral of a general cubic polynomial p(x) = Ax^3 + Bx^2 + Cx + D over the interval [-1,1].
By equating terms involving A, B, C, and D, and solving this system of equations, we would obtain the values for a, b, c, and d. However, the provided data snippet does not directly give us such constants, and as such, we cannot give a specific numerical value for d.