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Let f(x)=(x^(2)+2)/([x]),1 le x le3, whe...

Let `f(x)=(x^(2)+2)/([x]),1 le x le3`, where [.] is the greatest integer function. Then the least value of f(x) is

A

f (x) is increasing function

B

f (x) is decreasing function

C

The greatest value of `f(x) is (1)/(3)xx16.21`

D

The least value of f(x) is 2

Text Solution

Verified by Experts

The correct Answer is:
C
Here `f(x)=x^(2)+1,x lt x lt 2`
`(x^(2)+1)/(2),2 le x le 3 " " (x^(2)+1)/(3), 3 le x le 3.9`
`f.(x) gt 0` in each of the intervals and so f(x) is increasing in each of the intervals
`:.2 lt f(x) lt 5 "in" 1 le x lt 2, (5)/(2) le f(x) lt "in" 2 le x lt , (10)/(3) le f(x) le (1)/(3) xx 16.21 "in" 3 le x le 3.9`
Hence, the greatest value is `(1)/(3)xx16.21`
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