Let f(x) = vmatrix x^3 & x & x 6 & -1 & 0 p & p^2 & p^3 vmatrix , where p is a constant. Then d^3 dx^3 f(x) at x=0 is

JEE Advanced Mathematics question

Let

f(x) = ,

where is a constant. Then at is

Answer: (D)

Expand along the first row:

f(x) = - - 0) - x - 0) + x + p) = - - x + +p) x.

Differentiate three times:

f'(x) = - - x - +p) x,

f''(x) = - + x - +p) x,

f'''(x) = - + x

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Question ID VK-109237