Question

state and prove Lagrange's mean value theorem.

Answer 1

Hope that this will help you.

Answer 2

Mean is also called Average

Step-by-step explanation:

• The First Mean Value Theorem is also termed as Mean Value Theorem or Lagrange's Mean Value Theorem.

• The Process of searching for different mean values for different functions.

Lagrange’s Mean Value Theorem can be done as under -

For Function (f) in a closed interval (a,b), it should satisfy the following situations-

i) For closed interval (f) or function should be continuous.

ii) For open interval (a,b), we have a differentiable function.

$f'(c) = \frac {[f(b)-f(a)]}{(b-a)}$, is the condition which states x = c.

With the condition stated above (i) & (ii), we have 'c' in (a,b) interval but with one condition-

The tangent at c is parallel to the secant whose endpoints are (a,b)  

   f′(c) = $\frac {f(b)-f(a)}{b-a}$