Web Analytics
reggie98
Answered

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)

Verified Answer :

LammettHash

\(f(x)=\ln x\implies f'(x)=\dfrac1x\)
\(g(x)=x^2-1\implies g'(x)=2x\)

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

Related Questions