Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Maximum and minimum element.
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?
Equation
Roots
Algebra
But try the problem first...
Answer:S has a minimum but no maximum
B.Stat Objective Problem 715
Challenges and Thrills of Pre-College Mathematics by University Press
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.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
