1.

Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

Answer»

Solution :Let `f(x) = e^x/x^p`
Then ``f.(x) = (e^x CDOT x^p - e^x cdot px^p-1)/(x^2p)`
The FUNCTION is increasing if f. `(x) GT 0`
`RARR (e^x cdot x^p - e^x cdot px^p-1)/(x^2p)gt 0`
`(e^x cdot x^(p-1) cdot (x-p) gt 0 rArr x gt p.


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