# 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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