Comprehension

Let f(x) = (|x| - |x – 1|)2

What is f’(x) equal to when x > 1?

This question was previously asked in
NDA (Held On: 18 Sept 2016) Maths Previous Year paper
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  1. 0
  2. 2x - 1
  3. 4x - 2
  4. 8x - 4

Answer (Detailed Solution Below)

Option 1 : 0
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Detailed Solution

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Calculation:

f(x) = (|x| - |x – 1|) 2  when x > 1

For x > 1, |x| = x 

For x > 1, |x - 1| = (x - 1)

∴ f(x) = (x - ((x - 1)))2

⇒ f(x) = (x - x + 1)2

⇒ f(x) = (1)2

⇒ f(x) = 1

Now, f’(x) = 0

Hence, option (1) is correct.

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