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incg & decrg function

Asked by 29th May 2008, 8:17 AM
Answered by Expert
Answer:

is an increasing or decreasing function in a certain interval if +ve or –ve respectively in that interval because the tangent will make an acute angle for increasing function and obtuse angle for decreasing function. Hence,

= (+) for increasing functions and (-) for decreasing functions.

Remember: for all,                                                                                                                     

·         If is an increasing function then, .

·         If is a strictly increasing function then, .

·         If is an decreasing function then, .

·         If is a strictly decreasing function then, if.

Example:

For,

As a matter of fact we should say that, sin x is a strictly increasing function.

For,

.

 Thus, cos x is a strictly decreasing function.

Answered by Expert 29th May 2008, 11:44 AM
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