Functions : Maximum value of a function

Question 3
f(x) is defined as , x belongs to the set of natural numbers. For what value of x will f(x) be maximum?

1. 2
2. 3
3. 7
4. f(x) is a non-decreasing function. It has not definable maximum

Correct Answer is 3. Choice (2)

Explanatory Answer

Taking log on both sides,

Differentiating both sides,



.

When (1 - logx) = 0 or when x = e.

The function reaches a maxima at e, or is the highest value this function can take.

Within integer values, therefore, the answer can be either 2 or 3.

, so is greater than .

Anwer Choice (2).

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AIEEE Math Problems, Practice Questions and Answers : Listed Topicwise

Sets, Relations & Functions		Permutation Combination		Sequences & Series
Limits, Continuity & Differentiability		Statistics & Probability		Trigonometry
Mathematical Reasoning