Maximum and minimum value question

In summary, being differentiable at 2 means that the function has a slope of 0 at 2 and is continuous at that point. However, being continuous does not necessarily mean it is differentiable. When sketching a graph with a local maximum at 2 and being differentiable at 2, it is important to keep in mind the definition of differentiability and continuity, as well as ensuring the function appears "smooth" at 2.
  • #1
afcwestwarrior
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0
what does differentiable at 2 mean

what does this mean , my question says sketch the graph of a function who has a local maximum at 2 and is differentiable at 2,

what does it mean by it is differentiable at 2,
 
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  • #2
does this mean that the slope is 0 at 2
 
  • #3
well if u need to know what this means, it means if it is differentiable at 2 it is continuous at 2
 
  • #4
one more thing how do i sketch this graph, all it gives me is it is continuous at 2, does it matter how i sketch this graph, does it have to be a certain type, does it have to look a certain way, in the back of my book it is a parabola and its continuous on the negative side
 
  • #5
Well, differentiable and continuous is not equivalent. continuous if differentiable, but if continous, we can't conlude it is differentiable.
2 formulas below are definition of continuous and differentiable properties of a funtion, for example,F(x) :
+ F(x) is continuous at x0 <=> limit of F(x) when x->x0 is equal to F(x0)
+ F(x) is differentiable at x0 <=> limit of [F(x)-F(x0)]/[x-x0] when x->x0 exists (that value is so called F'(x0) )
Anyway, note that : "differentiable" and "continous" is not equivalent. "continous" if differentiable, but if "continous", we can't conlude it is differentiable.
If you have anymore question, feel confidently to ask me.
 
  • #6
Well, strictly speaking, it doesn't have to look particularly normal to satisfy the requirements. But likely for your purposes, you're going to want something that's continuous in an interval around 2 and appears "smooth" at 2 (i.e., it has no sharp edge).
 
  • #7
afcwestwarrior said:
does this mean that the slope is 0 at 2

Yes. It also means it is continuous at 2. Seeing as they had a parabola, it seems this function is one where the domain is limited.
 

What is the difference between maximum and minimum values?

The maximum value is the largest value in a set of data, while the minimum value is the smallest value in a set of data. They represent the upper and lower bounds of the data set.

How do you find the maximum value of a set of data?

To find the maximum value, you can either arrange the data in ascending order and choose the last value, or use a formula such as MAX() in a spreadsheet program.

Can there be more than one maximum value in a set of data?

Yes, there can be more than one maximum value if there are multiple data points with the same highest value in the set.

What is the significance of maximum and minimum values in data analysis?

Maximum and minimum values help to identify the range of data and can be used to detect outliers or unusual data points. They also provide a quick summary of the spread of the data.

How can you use maximum and minimum values to make decisions?

Maximum and minimum values can be used to compare data sets and determine which set has a larger or smaller range. They can also be used to set thresholds or limits for certain variables in a study or experiment.

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