Let , and be monotonically increasing function of x. Prove that increases with increase in .

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- May 11th 2009, 11:28 PMfardeen_genMonotonic functions?
Let , and be monotonically increasing function of x. Prove that increases with increase in .

- May 12th 2009, 04:25 AMPlato
- May 12th 2009, 05:51 AMfardeen_gen
I have no idea what the question means! Thats why I posted it.

- May 12th 2009, 10:05 AMpankaj
You are right Plato.

The question says that prove that increases as increases.

Let .

Therefore,

Let

(Using Leibnitz rule)

Given that ,therefore

Now,since is monotonically increasing,therefore

Hence,

Therefore, increases as increases

i.e. increases as increases.