Show that 5√(x² + 1) ≥ 3x + 4 for all x

[Dank2]

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?

 

[Ray Vickson]

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?

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.

 

[Dank2]

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.

thanks

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

 

[Ray Vickson]

thanks

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

Right!