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If x > 0, then which one is correct?(a) x > log(x + 1)(b) x < log (x + 1)(c) x = log(x + 1)(d) x ≥ log(x + 1)I got this question in an interview.My question comes from Calculus Application topic in section Application of Calculus of Mathematics – Class 12

Answer»

Right choice is (a) x > log(x + 1)

The EXPLANATION is: ASSUME, f(x) = x – log(1 + x)

THEREFORE, f’(x) = 1 – (1/(1 + x))

= x/(x + 1) > 0, when x > 0

Hence, we must have, f(x) > f(0), when x > 0

But f(0) = 0 – log1 = 0

Thus, f(x) > 0, when x > 0 i.e.,

x – log(1 + x) > 0, when x > 0

Or x > (1 + x), when x > 0.


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