Verifying the Correctness of Your Answer

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Homework Statement
Given the following graph, what are the intervals where the function is increasing, decreasing, or constant?
Relevant Equations
n/a
Screen Shot 2020-05-28 at 12.47.36 PM.png

Screen Shot 2020-05-28 at 2.32.42 PM.png

Is this answer correct?
 
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I see what you mean, but you should write OR instead of AND. The word AND corresponds to ##\cap## while OR corresponds to ##\cup##, which is what you need here.

So, to be totally clear, rather write: Increasing on ##[-4,-2]\cup [4,6]## and similarly for decreasing.
 
I'm not really sure, but if in ##x=-6## there is an asymptote, then the function is not defined in ##\left(-\infty,-6\right]##
 
What happened to (6,7]?
 
haruspex said:
What happened to (6,7]?
that is also increasing.
 
angela107 said:
that is also increasing.
Sure, just pointing out that you omitted it from your answer.
 
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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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