 Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Maximum and minimum element.

## Maximum and Minimum Element (B.Stat Objective Question )

A set S is said to have a minimum if there is an element a in S such that $a \leq y$ for all y in S. Similarly, S is said to have a maximum if there is an element b in S such that $b \geq y$ for all y in S. If S=$(y:y=\frac{2x+3}{x+2}, x \geq 0)$, which one of the following statements is correct?

• S has both a maximum and a minimum
• S has a minimum but no maximum
• S has a maximum but no minimum
• S has neither a maximum nor a minimum

### Key Concepts

Equation

Roots

Algebra

But try the problem first…

Answer:S has a minimum but no maximum

Source

B.Stat Objective Problem 715

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

y=f(x)=$\frac{2x+3}{x+2}$

or, $f'(x)=\frac{1}{(x+2)^{2}}>0$

Second Hint

So its a strictly increasing function

So it attains its minimum at x=0

Final Step

As given that function is defined on [0, infinity)

or, S has a minimum but no maximum.