Does this graph have any minimums or maximums?

- smurfy14

Does this graph have any minimums or maximums?

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- smurfy14

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- anonymous

min is -2 when x = -3

- anonymous

looks like no max but we only see part of the graph

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## More answers

- anonymous

(-3, -2) is the minumum but no maximum

- smurfy14

thats the whole graph i think it just keeps going

- smurfy14

thanks!

- anonymous

hold the phone. minimum means minimum value that y takes on. the minimum is not a coordinate. the minimum is a number. in this case it is -2

- anonymous

there is no minium

- anonymous

who's to say it continues in a postitve direction?

- anonymous

There is domain and range both of which have a minimum value in this case,

- smurfy14

wow im confused

- anonymous

the only information you know is that if it is a function x=-3 is the beggining of the domain
but yo udon't have any range info

- anonymous

This graph represents a function of x.
The domain of a function is all permissable values of x.
The range, all permissable values of y
Hence minimum value of x = -3 and minimum value oy y = -2

- smurfy14

hey gianfranco is what satellite said earlier true?

- anonymous

yes. this is a never ending source of confusion. the minimum is the output, not the input.

- anonymous

Of course, satellite is always right.

- anonymous

for example, if the function is \[f(x)=x^2-5\] the minimum value is -5

- anonymous

the fact that this function takes on the value of -5 when x = 0 does not make the minimum (0,-5)
the minimum is a number, not a coordinate

- anonymous

and no, i am often wrong!

- smurfy14

ok im going to take your word on it but what ecin is saying is reasonable too

- smurfy14

ah so what should i put as the answer??

- anonymous

I think it is better to acknowledge the point at which the graph takes a minimum vale which includses voth domain and range,

- anonymous

value

- anonymous

There is a minimum. There is no max because the graph appears to be cut off and 'continues' though we can't see it.

- smurfy14

um we kinda alread acknowledged that lol

- anonymous

there's no minimum

- anonymous

jesus

- anonymous

f(x) = x^2 -5 and it is said the minimum value is =-5
and to be clear you are saying the minimum value is the y value then
you are saying
f(-5) = (-5)^2 -5 which is not true.
this implies -5 = 20

- anonymous

oh. wait i didn't see the equation sorry

- anonymous

I just saw the graph lol

- smurfy14

ecin there was no equation

- anonymous

then there's no minimum

- anonymous

you don't know what happens outside. You are garanteed a min domain x-coordinate

- smurfy14

well given that the graph doesnt show which way it continues i think (-3,-2) is correct

- anonymous

that's my point exactly

- anonymous

Look at the graph Smurfy the dot at the left hand side implies there ore no lower points on the graph in terms of numerical value, so give both x and y values for sheer safety :)
The fact that there is no point on the right of the graph implies it goes on to infinity,

- anonymous

picture a capacitor graph before it discharges

- anonymous

you don't konw the lim x->inf

- smurfy14

gian you are right and based on http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx example four the minimum is probably x=-3

- anonymous

Definitely not probably I can assure you :)

- smurfy14

ok well should i pout x=-3 or a coordinate?

- smurfy14

*put

- anonymous

in example 4 . the x doesn't increase anymore showing you tahat theres o more inclrease or decrease

- anonymous

do what you want. I'm tired of arguing.

- anonymous

Coordinate but remember to state that it is a definite minimum, and importantly also state that there is no maximum.

- smurfy14

what do you mean by definite minimum? and ok

- anonymous

he means i'm wrong, where i stand on my belief i'm right

- anonymous

Well Ecin, the question doesn't ask about extemum, os the point would at least be considered relative minimum.

- anonymous

it's a local min for sure

- anonymous

This is getting a little heavy. Look at the graph. It is not complicated. It shows that the graph does not extend beneath the coordinate (-3, -2) and also it does not 'appear' to have a resting place in the first quadrant .

- anonymous

the minimum value means the minimum output, not the minimum input. if your domain is all real numbers then there is no minimum input. so say that the minimum value of \[f(x)=x^2-5\] is -5 means this is the smallest output you can get. it does not say that the minimum possible value of x is -5, nor does it say what \[f(-5)\] is

- anonymous

if you are taking calc you will frequently have to find the maximum or minimum value of a function. to do this you will probably have to find the value of x that gives it to you. say the minimum values occurs when x = 7. that does not mean the minimum value is 7. that means the minimum value is f(7) whatever that may be.

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