Question

Let f(x)=(x^2)-sqrt(x).
-show that x^2< or equal to f(x) for all x> or equal to 0
-use the inequality in the first part to to show that the integral of 1/f(x) from 1 to infinity converges.

How do you start this?

Answer 1

\(f(x)=x^2-\sqrt{x}\)
domain-> [0,infty)
for x>1,f(x)>0
for x=1, f(x)=0
for 0<x<1, f(x)<0

Answer 2

\[\sqrt{x}=x^2-f(x)>0\]
since square-root cannot be negative