decreasing function

Question

How to Calculate?

f(x) is decrasing in $[3,\alpha ]$

then f(x) is continuous or not continuous on x=5?

Comments

what is $\alpha$ and what is $f(x)$ ?

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f(x) is a function

$\alpha$ actually infinity

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answer is continuous right?

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no..

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all monotonic functions are continuous in there interval http://math.stackexchange.com/questions/103630/proving-continuity-with-monotonic-functions so it should be continuous

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if α<5 we cant say anything about the behaviour at x=5. may or may not be continuous.
but if α>5 i think it should be continous.

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yes, go for detail plz

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oh thats infinity.. i was thinking its alpha 
if that is infinity i think it should be continous
If f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. means tangent should exist at each point. as its given that it is decreasing function, tangent exist at every point even at x=5. so it should be continous 

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If tangent exists it is differentiable at that point if it is differentiable then it is continuous

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yes.

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It may or may not be .. We can have discontinuous graph still satisfying decreasing function property..As basic definition is :

f(x) is strictly increasing if f(a) > f(b) for all a < b.
f(x) is increasing if f(a) >= f(b) for all a < b.

rather than in terms of f'(x)..

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Without graph if any other way to derive it

Like with function

Can u give an example

if example possible for f(a) > f(b) for all a < b.