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f(x)=(x-2)|x-3| is monotonically increas...

`f(x)=(x-2)|x-3|` is monotonically increasing in `(-oo,5/2)uu(3,oo)` (b) `(5/2,oo)` `(2,oo)` (d) `(-oo,3)`

A

`(-oo,5//2)cup(3,oo)`

B

`5//2,oo)`

C

`(2,oo)`

D

`(-oo,3)`

Text Solution

Verified by Experts

The correct Answer is:
1
`f(x) =(x-2)|x-3|`
For f(X)=(x-2)(x-3)=`x^(2)-5x+6`
`f(X)=2x-5=0 or x=5//2`
Now the graph of f(X) =(x-2)|x-3is as follows

Clearly from the graph f(X) increases in `(-oo,5//2)cup(3,oo)`
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