MathDB

11.2

Part of 2006 Moldova National Olympiad

Problems(1)

Exists c, f'(c)=...

Source: Moldavian MO 2006

3/19/2006
Function f:[a,b]→Rf: [a,b]\to\mathbb{R}, 0<a<b0<a<b is continuous on [a,b][a,b] and differentiable on (a,b)(a,b). Prove that there exists c∈(a,b)c\in(a,b) such that f′(c)=1a−c+1b−c+1a+b. f'(c)=\frac1{a-c}+\frac1{b-c}+\frac1{a+b}.
functionlimitreal analysisreal analysis unsolved