Answer to Question #154260 in Differential Equations for mafizur alam

Question

if from mean value theorem, f(x1)=f(b)-f(a)/b-a, then

Answer 1

if from mean value theorem, $f(x_1)=\frac{f(b)-f(a)}{b-a}$, then

$\implies x_1$ is in an interval

Mean Value Theorem

1. f(x) $\to$ continuous in [a,b]
2. f(x) $\to$ diff in (a,b)
3. $f'(x)=\frac{f(b)-f(a)}{b-a}$

$$\\a<x<b\\ a<x_1<b\\$$