Let f(x)= vmatrix x^3&x^2&3x^2 1&-6&4 &p^2&p^3 vmatrix

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

Let

f(x)=\begin{vmatrix}x^3&x^2&3x^2\\1&-6&4\\p&p^2&p^3\end{vmatrix},

where

p

is a constant. Then

\frac{d^3f(x)}{dx^3}

is: (a) Proportional to

x^2

(b) Proportional to

x

x^3

(d) A constant