Mathematics 45 Online
OpenStudy (anonymous):

can anyone explain the concept of maxima and minima?

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

OpenStudy (anonymous):

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

OpenStudy (anonymous):

are you in calculus?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

yes... can you explain a bit more?

OpenStudy (anonymous):

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.

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

okay friends all right thanks

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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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