can anyone explain the concept of maxima and minima?

when you are at the top of a hill; youve reached the maximum height around you when your in the valley, you are standing at the minimum height of the land around you

the tallest person around is at the maximum height the shortest person is the minimum height ...

What about the tallest midget?

i get it already but what i wanna ask is in terms of functions

are you in calculus?

ok ..... um. the greatest value the function gives is the maximum. and the lowest value it gives is the minimum .. maybe?>

yes... can you explain a bit more?

Minimum and maximum refers to the points on the graph when the slope is equal to zero; the graph is neither increasing nor decreasing anymore. The tangent line to the graph is parallel with the x-axis.

i dont think I can explain it anymore without getting specific references from you

min and max have zero slopes yes; but a zero slope does not guarenttee a min OR a max

When you take derivative and set that derivative equals to 0, you will find either min or max

If you want to know which one it is, compare it with an arbitary point.

f'(x) = 0 is a critical point, but may NOT be a min or a max f'(x) = undefined is also a critical point, but not a guarentee

Yep, in order to really know if the point is a max or min, you must also graph the function or otherwise know the behavior of the function.

okay friends all right thanks

the behaviour of the function is the most telling of min and max :)

if f'(x) = 0 and the sign of f'(x) differs on the left and the right; your at an extrema

+ to - is a max - to + is a min

Yep, in order for a point to qualify as a max or min, the graph must be continuous and defined at that point.

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