## Carissa15 one year ago Apply the mean value Theorem to f(x)=In(1+x) to show that x1+x<ln(1+x)<x,forx>0. I am still unsure of this, I think I need to substitute any x>0 for each of the 3 equations and their derrivative x1+x<ln(1+x)<x to prove that for any x > 0 each equation will be less than the last?

1. Carissa15

$f(x)=\ln(+x)$ is the original equation and I have to use the mean value theorem to show that$\frac{ x }{1+x } < \ln(1+x) < x,$ for x > 0.

2. IrishBoy123

I'm on mobile and can't do any latex or drawing So, to solve note simple statement of MVT: f'(c) = [ f(b) - f(a) ] / [b -a] Using a = 0, b = x, calculate f'(c) in terms of x. Then look separately at inequalities (A) c< b, ie c< x and (B) c> a,ie c> 0 Some faffing around and you will get there

3. Carissa15

Thank you so much, all sorted now. Big help. Thanks