Some tangent slope equals the secant slope across the interval.Suggest a slogan
Let \(a<b\) and let \(f\colon[a,b]\to\RR\) be continuous on \([a,b]\) and differentiable on \((a,b)\). Then there exists \(\xi\in(a,b)\) such that \[ \frac{f(b)-f(a)}{b-a}=f'(\xi). \] [@Rud76].