Compare two functions.

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– Posted on 09/05/2014Posted in: MATH

For the given functions f:y=\frac{2x^{2}+5x+3}{2x+1}  and  g:y=5x . a)Show that in [1;+∞[ , f(x)≤g(x).

To compare two functions,make their difference.

f(x)-g(x)=\frac{2x^{2}+5x+3}{2x+1}-5x=\frac{2x^{2}+5x+3-5x(2x+1)}{2x+1}=\frac{2x^{2}+5x+3-10x^{2}-5x}{2x+1}=\frac{-8x^{2}+3}{2x+1}<0 for  x≥1.

 

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