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NDA2016MathematicsDeterminantsActual

Consider the function f(x)= | array ccc x^3 & x & x 6 & -1 & 0 p & p^2 & p^3 array | , where p is a constant. What is the value of f ^ (0) ?

Options

  1. Ap ^3
  2. B3 p^3
  3. C6 p ^3
  4. D-6 p^3

Correct answer

D. -6 p^3

Step-by-step solution

aligned f(x) & = | array ccc x^3 & x & x 6 & -1 & 0 p & p^2 & p^3 array | f^ (x)= & | array ccc 3 x^2 & x & - x 6 & -1 & 0 p & p^2 & p^3 array |+ | array ccc x^3 & x & x 6 & -1 & 0 0 & 0 & 0 array | & + | array ccc x^3 & x & x 0 & 0 & 0 p & p^2 & p^3 array | aligned aligned f^ (x) & = | array ccc 3 x^2 & x & - x 6 & -1 & 0 p & p^2 & p^3 array | f^ (0) & = | array ccc 0 & 0 & - 0 6 & -1 & 0 p & p^2 & p^3 array | & =-6 p^3 aligned

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