State the Langrage mean value theorem .Hence show that
, x>0
next, you should state completely what the mean Value Theorem says since you have stated/used only part of it.
Then, from the equation you posted it follows that (the steps should be basic at this level and are left for you to fill in). Since c > 0 the required result easily follows.
Solution :
Here
Using Lagrange Mean value theorem
and
.............(1)
Differentiating wrt x weget
..........................(2)
Now comparing eq(1) and (2) weget
..........[since ]
.............................(3)
Taking c = 0 eq (3) becomes
......................................(4)
Taking c = x in eq(3) weget
..............................(5)
Therefore u can see that the 2 term is less that the first term
............................(6)
Now from (4) and (5) we can write the same eq (6) as