# Understand the problem

f(x) =

.

Determine the set {y ∈ R : y = f(x), x ≥ 0}.

##### Source of the problem

I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2013. Subjective Problem no. 2.

##### Topic

##### Difficulty Level

Medium

##### Suggested Book

# Problems In CALCULUS OF ONE VARIABLE

by

# Start with hints

Do you really need a hint? Try it first!

This problem simply ask for the range of the function defined by f(x)=

compute the derivative of the function =

First extrema occurs at =

The first derivative is negetive in the interval [ 0, ]

hence the function is decreasing in this interval

f(0)= ; f()=

For x>

the derivative becomes positive , and remain so upto x= after which it becomes negative

thus we have minima at x= and maxima at x=

f()=

note that as the denominator of the function increases

Hence we can conclude that

clearly x= gives the global maxima

so , the range is (0,]

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