Finding Intervals for Increasing and Decreasing Functions of a Cubic Equation

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hi, I'm not good at math at all. and I'm not sure how to finish this equation. any help would be appreciated. Thanks.



I need to find the intervals of where the function is increasing and decreasing.

f(x)= 2x3 - 5x2 - 4x + 2
 
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Well first you need to differentiate it. What do you think you should do after that?
 
You need first to construct a table for that and find the roots of the equation and its differentials.
 

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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