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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 p for which f^ (0)=0 ?

Options

  1. A- 1 6 or 0
  2. B-1 or 0
  3. C- 1 6 or 1
  4. D-1 or 1

Correct answer

A. - 1 6 or 0

Step-by-step solution

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

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