i would like to ask question about unimodality of probability function ,from wikipedia
http://en.wikipedia.org/wiki/Unimodal
it says that In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object,there is also picture of this one maximum value of probability function
it can have of course several mode,as
Strictly speaking, a mode of a discrete probability distribution is a value at which the probability mass function (pmf) takes its maximum value. In other words, it is a most likely value. A mode of a continuous probability distribution is a value at which the probability density function (pdf) attains its maximum value. Note that in both cases there can be more than one mode, since the maximum value of either the pmf or the pdf can be attained at more than one value.
If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal".
but i want to ask question according fucntion,because we know that function reaches it's maximum at this point where it's derivative is equal to zero or it is undefined(critical point),now does unimodal function have derivative?is it continuous?could you help me to answer these questions with several examples?thanks in advance