If the derivative of the function\(f(x) =\frac{m}{x} +2nx + 1\) vanishes at x = 2, then what is the value of m + 8n ?

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Question

This question was previously asked in

NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)

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Answer 1

Calculation:

⇒ \(\displaystyle f(x) =\frac{m}{x} +2nx + 1\)

⇒ \(\displaystyle f'(x) =\frac{-m}{x^2} +2n\)

Since the derivative vanishes at x = 2, f'(2) = 0

⇒ \(\displaystyle f'(2) =\frac{-m}{2^2} +2n=0\)

⇒ \(\displaystyle f'(2) =\frac{{-m} +8n}{2^2}=0\)

⇒ m = 8n

∴ Value of m + 8n cannot be determined due to insufficient data.