Question

When does value of local minima greater than local maxima?

Answer 1

Local minima and maxima:-

A function ff has a local maximum or relative maximum at a point xoxo if the values f(x)f(x) of ff for xx ‘near’ xoxo are all less than f(xo)f(xo). Thus, the graph of ff near xoxo has a peak at xoxo. A function ff has a local minimum or relative minimum at a point xoxo if the values f(x)f(x) of ff for xx ‘near’ xoxo are all greater than f(xo)f(xo). Thus, the graph of ff near xoxohas a trough at xoxo. (To make the distinction clear, sometimes the ‘plain’ maximum and minimum are called absolute maximum and minimum.)

Yes, in both these ‘definitions’ we are tolerating ambiguity about what ‘near’ would mean, although the peak/trough requirement on the graph could be translated into a less ambiguous definition. But in any case we'll be able to execute the procedure given below to find local maxima and minima without worrying over a formal definition.

hope this helps u... .