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Algebra Arithmetic Calculus I.S.I. and C.M.I. Entrance ISI Entrance Videos

Maximum and Minimum Element | TOMATO BStat Objective 715

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Maximum and Minimum Element. You may use sequential hints.

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

Check the Answer


But try the problem first…

Answer:S has a minimum but no maximum

Source
Suggested Reading

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.

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