# Homework Help: Showing that a Parabola's y values are greater than or equal to a line's y values

1. Dec 12, 2016

### Dank2

1. The problem statement, all variables and given/known data
the two functions $$f(x) = 5(√(x^2 +1))$$ $$g(x) = 3x + 4$$.

2. Relevant equations

3. 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?

2. Dec 12, 2016

### Ray Vickson

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.

3. Dec 12, 2016

### Dank2

thanks

its point 3/4. and it is the absolute minimum of the graph that's equal to 0, therefore f(x) >= g(x).

4. Dec 13, 2016

Right!