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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?

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  1. Carissa15
    • one year ago
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    \[f(x)=\ln(+x)\] 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
    • one year ago
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    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
    • one year ago
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    Thank you so much, all sorted now. Big help. Thanks

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