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• #1472

It is not quite clear what sort of question you are referring to but the he question seems to be about giving the points where a function is greater than zero. Is that what you are asking?

If so, first you need to solve the equation g(x)=0. Then you need to sketch a graph of the function and consider where the graph is above the x-axis giving g(x)>0 and where it is below the x-axis giving g(x)<0. The solutions will be on one side or the other of the points where the graph cuts the x-axis or maybe between those points according to the function.

• #1596

Thanks Toni ,if you are given f(x).f(x)<0 f is having a prime that it is a derivative the other f is a function how do you intepret it given a cubic function ,i am having a problem in notatiÃ¶n and explaining in using maths language

• #1597

I think you are asking the following question “How do I interpret the information that f(x) is a cubic polynomial and the derivative f ‘(x)<0 [which can also be written df/dx<0]?”

This is telling you that the derivative is negative so the function is decreasing. If you are given the equation you ought to be able to differentiate it and find when f ‘(x) = df/dx = 0. From this can you find the maximum and minimum points? With that information can you sketch the graph and find the values of x for which the function is decreasing and df/dx<0? I hope this helps.

• #1603

Thanks a lot ive been trying to answer the questiÃ¶ns on functions having inequalities

• #1629

I think these interpretations confuse many especially in trig functions where people take the dot to mean ‘and’ instead of an inequality form. I think in our next residential course there must be some input from aimssec or such questions should be part( i suggest), So that people can come to terms to terms with such questions. It is not Ntyantyi’s problem alone.

• #1635 Anonymous

Hi
When I read through these posts on functions I noticed how hard it was to write formal mathematical statements without all the symbols we need. Using an apostrophe for the derivative f'(x) seeems a good idea. Once the problem is described in words it seems easier to think about. This is often what the teacher does. The learner stares at the problem and doesn’t know how to start. The teacher describes the problem in words and suddenly the learner can get started. Do people have ideas for helping the learners to be more independent? This is the sort of thing I mean:

At the start of a lesson write 3 similar problems in formal notation on the board. Tell the learners they are NOT to solve the problems. Working in pairs the learners discuss:

1. What the notation means
2. What you have to find.
3. The things you will have to do to solve the problems.

The important thing is for the learners to talk about the problems. Listen in to their discussions and choose some pairs to present their ideas to the whole class.

Now continue with the lesson. Solving the problems could be left for homework.

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