reggie98
contestada

Calculus help??????

the functions

f(x)= ln(x) and g(x)= x^2-1

they are both 0 when x=1

apply the Race Track Principle to explain which of the following inequalities is true for x is (greater than or equal to) 1:

f(x) < g(x)
or
g(x) < f(x)

Respuesta :

LammettHash
[tex]f(x)=\ln x\implies f'(x)=\dfrac1x[/tex]
[tex]g(x)=x^2-1\implies g'(x)=2x[/tex]

You have [tex]2x^2>1[/tex] for all [tex]x\ge1[/tex], and dividing by [tex]x[/tex] gives [tex]2x>\dfrac1x[/tex], or [tex]g'(x)>f'(x)[/tex]. By the racetrack principle, then, it follows that [tex]g(x)>f(x)[/tex].

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