Question

According to Lagrange's mean value theorem, given that all conditions are satisfied for f(x) in the interval $[a,b]$, there exists at least one c such that f'(c) = , where $a<c<b$

• A. $\frac{f\left(b\right)-b}{f\left(a\right)-a}$
• B. $\frac{f\left(b\right)-f\left(a\right)}{b-a}$
• C. $\frac{f\left(a\right)-f\left(b\right)}{b-f\left(a\right)}$

Answer 1

The correct option is B $\frac{f\left(b\right)-f\left(a\right)}{b-a}$

According to Lagrange's mean value theorem, if f(x) is continuous in the interval [a,b] and differentiable in the interval(a,b), then there exists at least one value of c such that $a<c<b$ and $f^{\prime }\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$