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Let f(x) =xsqrt(4ax-x^(2)),(agt0) Then f...

Let f(x) =`xsqrt(4ax-x^(2)),(agt0)` Then f(x) is

A

increasing in (0,3a) decreasing in (3a,4a)

B

increasing in (a,4a),decreasing in `(5a,oo)`

C

increasing in `(0,4a)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1
f(X)=`xsqrt(4ax-x^(2))`
`therefore f(X) =sqrt(4ax-x^(2))+x(4a-2x)/2sqrt(4ax-x^(2))`
`=(2x(3a-x))/sqrt(4ax-x^(2))`
Now if `f(X)gt0` then
`2x(3a-x)gt0`
`2x(x-3a)lt0`
or x in (0,3a)
Thus f(x) increases in (0,3a) and decreases in (3a,4a)
Thus f(X) increases in (0,3a) and decreases (3a,4a)
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