Differentiation problem and finding maximum, ing ?

JakePearson
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Differentiation problem and finding maximum, need helping :)?

have a few problems with these questions, can you help :)

Using differentiation, find the MAXIMUM value of the following functions?

1. f(x) = x2 / 4 + 4 / x
2. f(x) = xe-2x2
3. f(x) = sqrt(x - n) / x ; n>0

hope you guys can help !
 
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JakePearson said:
have a few problems with these questions, can you help :)

Using differentiation, find the MAXIMUM value of the following functions?

1. f(x) = x2 / 4 + 4 / x
2. f(x) = xe-2x2
3. f(x) = sqrt(x - n) / x ; n>0

hope you guys can help !

We can help, but only after you show us how you would approach them. How do you find the min and max of functions?
 
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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