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NDA2026MathematicsDeterminantsActual

Let f(x)= vmatrix 3x^2 & x & - x 6 & -1 & 0 q & q^2 & q^3 vmatrix where q is any constant, then what is d^2 dx^2 (f(x) ) at x=0 equal to ?

Options

  1. A-1
  2. B0
  3. C1
  4. Dq

Correct answer

B. 0

Step-by-step solution

Given the function f(x) as a determinant where only the first row contains the variable x : f(x)= vmatrix 3x^2 & x & - x 6 & -1 & 0 q & q^2 & q^3 vmatrix To differentiate the determinant with respect to x , we differentiate the elements of the first row while keeping the other rows unchanged. Differentiating once with respect to x : f'(x)= vmatrix 6x & - x & - x 6 & -1 & 0 q & q^2 & q^3 vmatrix Differentiating again with respect to x : f''(x)= vmatrix 6 & - x & x 6 & -1 & 0 q & q^2 & q^3 vmatrix Substituting x=0 in

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