applied extrema project

[ahenriques12cc]

I had to differentiate a function using two different methods, which i did just fine. The project also asks "discuss the domain of your function in some detail (discrete, continuous, integral, positive or negative, restrictions)"

I don't know what most of these terms mean.

The function is : f(x)= 15 / (x^2 -4x+5)

I determined that it is continuous and the restrictions for the particular problem i was given. So i need to know if it is integral, and positive or negative!

 

[pappus]

I had to differentiate a function using two different methods, which i did just fine. The project also asks "discuss the domain of your function in some detail (discrete, continuous, integral, positive or negative, restrictions)"

I don't know what most of these terms mean.

The function is : f(x)= 15 / (x^2 -4x+5)

I determined that it is continuous and the restrictions for the particular problem i was given. So i need to know if it is integral, and positive or negative!

Re-write the equation of the function:

\(\displaystyle \displaystyle{f(x)=\frac{15}{x^2-4x+5} = \frac{15}{x^2-4x+4+1} = \frac{15}{(x-2)^2+1}}\)

The sum of a square and a positive number is always positive, so ....