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Question

The function which is neither decreasing nor increasing in π2,3π2 is:


A

cosecx

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B

tanx

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C

x2

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D

x-1

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Solution

The correct option is A

cosecx


Explanation for the correct option:

We can identify the function by drawing the graph of the given options between the given range.

The given range is π2,3π2

Option (A): Draw the graph of cosecx

Here, in the graph we can clearly observe that the graph of cosecx increasing inπ2,ππ,3π2.

But around x=π

f(π-)>f(π+)

So, cosecx is neither increasing nor decreasing in π2,3π2.

Thus, option (A) cosecx is the correct answer.

Explanation for incorrect options:

Option (B): Graph of tanx between π2,3π2

As the graph shows, it is increasing between π2,3π2.

So, the given option is incorrect.

Option (C): The given option is x2

Now for positive value of x,x2 is always increasing function.

As, f'(x)=2x>0x>0

Thus, the function will be increasing. So, the given option is incorrect.

Option (D): For the given option, x-1,

For x>1,the function is increasing as f'(x)=1 and x=π2>1.Therefore fucntion will increase in the given interval.

Thus, option (D) is incorrect as well.

Therefore, the correct option is (A).


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