In: Advanced Math
Use the Mean-Value Theorem to prove that 30/203 < √ 103 − 10 < 3 /20 .
Solution: Let (where ) be any two distinct points of , then by Lagrange's mean value theorem, we get
or
Let , then for so that .
Then from above, we can write
--------------------------------(a)
Again, for so that . Then from above, we can write
........................................(b)
Combining (a) and (b), we obtained the required result