# What articles (if any) are needed in "...achieve __ maximum value in __ function"?

1. "We derive a condition to achieve the maximum value in a function"

versus

1. "We derive a condition to achieve a maximum value in the function"

versus

1. "We derive a condition to achieve maximum value in a function"

which is correct?

My first concern is whether to use "the function" or "a function". I understand "the function" is implying reference to the specific function. However, the function I have in mind is a generic function that models some events. So depending on the event, the generic function is changed. On the other hand, implying reference to the specific generic function is also correct. So is there a grammar rule to determine whether to use "the function" or "a function"?

My second concern is whether to use "the maximum value", "a maximum value" or "maximum value". Since I can have many different functions, I have many different maximum, so "a maximum" seems to make sense. But grammar checks tools are telling me to use "maximum" without the article. So which is correct?

• You have answered your own question. If you have not actually mentioned the specific function, it is a function. It then becomes the function. The a shifts to the. I had a mouse in my house. The mouse was very cute. :) Nov 14, 2019 at 23:21

I think you have two non-dependent issues, which is where the confusion may come from:

1. Is there only one generic function or are there more than one possible functions from which to choose? If there is only one, use the definite article - "the generic function". If there are a few to choose from, use "a generic function." or "the most appropriate generic function."
2. Whichever function you use, is there only ever one possible maximum value, or could there be more than one, for example + / - 50? If there can only ever be one maximum value, then it should be the definite article - "the maximum value..." If there could be more than one maximum - "a maximum value..."

Your third option: "We derive a condition to achieve maximum value in a function." [To me] is not speaking about a maximum numerical value obtained from operation of the function, but more about getting the most benefit out of using the function, some 'value for money' or 'cost vs benefit' assessment of the function's operation. I'm not sure this is what you want...

It will probably be clearer if you also include the dependancy information about the different values / events and the fact that the function is generic, rather than specific.

So, if there is only one generic function and one maximum value for that function, you could say:

"We derive a condition to achieve the maximum value using the generic function."

If there are a number of generic functions from which to chose, but only one maximum value, you could say:

"We derive a condition to achieve the maximum value using the most appropriate generic function."

or

"We derive a condition to achieve the maximum value using a generic function."

The maximum value for the chosen event is definite, but the event is indefinite - it depends which one you choose...

or possibly:

"We derive a condition to achieve an event-dependent maximum value using a generic function."

Both the event and maximum value are indefinite - it depends which one you choose...

• If there is only one generic function, you still start with a function. There is a function such that [whatever]. The function [does whatever]. You only start with the function in cases that are known: The x function [is whatever]. Nov 15, 2019 at 0:01
• If you say so... Nov 15, 2019 at 17:02
• "We derive a condition to achieve the maximum value of a function. The function [etc.] Is that not correct? Nov 15, 2019 at 17:10
• The poster says that the generic function is modified by the event and that the value of the function changes, dependent upon the event . What is the point you are trying to make? I don't understand... Nov 15, 2019 at 17:48
• My points are purely grammatical. In English, if one starts by positing a generality ("We derive a condition [...]"), that generality will then be followed by a specific condition. A condition then becomes the condition in the ensuring sentence. English speakers do this naturally,without even realizing it. Non-native speakers have no idea about it. Nov 15, 2019 at 18:48