# real analysis – Prove \$f(1)-f(-1)>f’left(-frac{1}{sqrt{3}}right)+f’left(frac{1}{sqrt{3}}right)\$.

Suppose the 5th order derivative function of $$f(x)$$ ,say, $$f^{(5)}(x)>0$$ for $$xin (-1,1)$$.Prove $$f(1)-f(-1)>f’left(-dfrac{1}{sqrt{3}}right)+f’left(dfrac{1}{sqrt{3}}right)$$.

I know this can be done directly by Gauss-Legendre formula, but does there exist a more elementary proof?