Prove-that-if-p-gt-q-gt-0-and-x-0-1-p-x-p-p-1-1-1-q-x-q-q-1-1-

Question Number 13731 by prakash jain last updated on 22/May/17

Prove that if p > q > 0 and x ⩾ 0

\frac{1}{p} (\frac{x^{p}}{p + 1} - 1) ⩾ \frac{1}{q} (\frac{x^{q}}{q + 1} - 1) .

Commented by mrW1 last updated on 25/May/17

f u n c t i o n f (x) = \frac{1}{x} (\frac{a^{x}}{x + 1} - 1) i s f o r

x > - 1 i n c r e a s i n g, s o f (p) > f (q) .

w e m u s t o n l y p r o v e t h a t f^{'} (x) > 0 .

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