The discussion revolves around comparing two functions, f(x) = 5(√(x^2 +1)) and g(x) = 3x + 4, to determine if f(x) is greater than or equal to g(x) for all x in the real numbers. Participants are exploring the characteristics of these functions, particularly focusing on their minimum points and tangential behavior.
The discussion is ongoing, with participants sharing insights about the minimum point and tangential behavior of the functions. There is no explicit consensus yet, but some guidance has been offered regarding the analysis of the difference function.
There is a note regarding terminology, specifically the correct use of "parabola" instead of "parabula," indicating a focus on precise mathematical language. Additionally, the participants are working within the constraints of a homework assignment, which may limit the depth of their exploration.
Dank2 said:Homework Statement
the two functions f(x) = 5(√(x^2 +1)) g(x) = 3x + 4.Homework Equations
The Attempt at a Solution
I can get the minimum point of f(x) and it is bigger than g(x) and that point, however g(x) is tangential to the curve f(x) at point 3/4.
what else do i miss to show that f(x) is bigger or equal than g(x) for all x in R?
thanksRay Vickson said:Find the minimum of the difference function ##f(x) - g(x) = 5 \sqrt{x^2+1} -(3x+4)##.
BTW: the word is parabola, not parabula; and anyway, you do not have a parabola anywhere in this problem.
Right!Dank2 said:thanks
its point 3/4. and it is the absolute minimum of the graph that's equal to 0, therefore f(x) >= g(x).