Proving Inequality using Mean Value Theorem

[frankpupu]

Homework Statement

Use the Mean Value Theorem to prove that if p>1.then ((1+x)^p)>(1-px) for x in (-1,0)and(0,infinite)

i have no idea that what's the relationship between the inequality and the theorem? first i define g(X)=((1+x)^p)-(1-px) then for x=0 f(0)=0.i.e. x not equals to 0,which x is in(-1,0)and(0,infinite), then i don't know how to do next ,i think is that one case for x>0 ,the other is for -1<x<0, then use theorem to prove g(X)>0 can someone give me some idea?

 

[LCKurtz]

Homework Statement

Use the Mean Value Theorem to prove that if p>1.then ((1+x)^p)>(1-px) for x in (-1,0)and(0,infinite)

i have no idea that what's the relationship between the inequality and the theorem? first i define g(X)=((1+x)^p)-(1-px) then for x=0 f(0)=0.i.e. x not equals to 0,which x is in(-1,0)and(0,infinite), then i don't know how to do next ,i think is that one case for x>0 ,the other is for -1<x<0, then use theorem to prove g(X)>0 can someone give me some idea?

It isn't true if $p=2$ and $x=-1/2$.