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incg & decrg function
Asked by | 29 May, 2008, 08:17: AM

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 | 29 May, 2008, 04:19: PM

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