Q. 3 TB - Calculus

Question

State the Mean Value Theorem.

Step-by-Step Solution

Answer

The mean value theorem state that if a function f is continuous on the interval $[a,b]$and differentiable on $(a,b)$then there will be at least one value c that belongs to the interval such that,

$$\begin{gathered} f\text{'}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a} \\ \mathrm{Where} c\in (a,b) \end{gathered}$$

Step 1. Given information.

The given theorem whose description is asked is Mean Value Theorem. 

Step 2. Description.

Mean Value Theorem. 

Consider a function $f\left(x\right)$is continuous on the interval $\left[a,b\right]$and differentiable on $\left(a,b\right)$then there will be at least one value c which belongs to the interval such that,

$$\begin{gathered} f\text{'}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a} \\ \mathrm{Where} c\in (a,b) \end{gathered}$$