The question is
the interactions at a social gathering follow the mathematical progression N(t)=30t-t^2, where t is the time in minutes since the party began, and N is the number of separate conversations occuring. what is the maximum number of interactions? thats all the information i was given. I'm not sure what to do with this problem
Sorry I should probably mention about minimum values.
If you differentiate your original function, set equal to zero and solve, you may get 1, 2 or inifite solutions, depending on the type of your equation.
To check whether it is a maximum or minimum value you that you have found, you take the second derivative and then substitute in your value(s) again.
If the function is less than 0, then it is a maximum, if it is greater than zero then it is a minimum.
Hope that wasn't too confusing
thank you so much, i dont know why i found it so difficult, i kept forgetting to carry the 2 when a function is squared to calculate the derivative. I have another question that is similar except my derivative doesnt leave me with much. its to maximize revenue and the function is 1200(1.50-x)
However as this is extremely similar to your original I'll just answer it here.
As you will have noticed when you differentiate it, the variable (x) disappears, in this case, there is no maximum as the function is unbounded, so the answer is infinity or undefined.