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Comprehension

Consider the function  

, where p is a constant

What is the value of f’(0)?

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NDA (Held On: 17 April 2016) Maths Previous Year paper
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  1. p3
  2. 3p3
  3. 6p3
  4. -6p3

Answer (Detailed Solution Below)

Option 4 : -6p3
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Detailed Solution

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Concept:

Differentiation of the determinant of a matrix: Differentiate the first row (or column) and keep the entries of the other row untouched. Do this for all other rows (or columns). Then find the sum of all such determinants. Then you can get a determinant.

Calculation:

Given:

Differentiate with respect to x, we get

 

  

Put x = 0, we get

 

⇒ f’(0) = 0 – 1(6p3 – 0) + 0

∴ f’(0) = - 6p3

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