Proving Increasing Function: f'(x)=f(x) for all x

kmeado07
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Homework Statement



Let f : R(real numbers) (arrow) (0,infinity) have the property that f ' (x) = f (x) for all x. Show that f is an increasing functions for all x.

Homework Equations





The Attempt at a Solution



I know that if f ' (x) > 0 , where all of x belongs to a,b (not bounded) then f is strictly increasing on [a,b].

So i need to show that f(x) > 0 maybe?

Any help/guidelines would be much appreciated.
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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