Re: 2012 HSC MX2 Marathon
Let f(x)=cos(x)-1+(x^2/2)-(x^4/24)
When x=0, f(x)=f(0)=0
f '(x)=-sin(x)+x-(x^3/6)
f ''(x)=-cos(x)+1-(x^2/2)
f '''(x)=sin(x)-x
Note that y=x is the tangent to y=sin(x) at x=0 meaning that x>sin(x) <=> sin(x)-x<0 for all x>0.
In order to prove the statement for x>0...