Please explain graphically the above changes(I imply changes in roots, derivatives at some points, continuity and differentiability at some points etc
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$\begingroup$ I cannot see a question here. $\endgroup$– Martin RJan 7, 2018 at 18:52
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$\begingroup$ I mean any function not very specific, I request you to answer my query using various functions as examples. $\endgroup$– Krishna DeshmukhJan 7, 2018 at 18:54
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2 Answers
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Take the function $f(x) = 1$ if $x$ is rational and $-1$ if $x$ is irrational. Then $f$ is no where differentiable or continuous, and its graph has no tangent lines anywhere.
But $f^2(x) =1 $ for all real $x$, so it's differentiable and continuous everywhere and has a tangent at every point.
answered Jan 7, 2018 at 18:58
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$\begingroup$ It's pretty easy to graph the function $y=1$ and observe its various properties. $\endgroup$ Jan 7, 2018 at 19:36
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If y is f(x) then
$$(y^2)^{'} = 2 y y^{'}$$
The place where max/min occurs (x coordinate) is unaffected. But max / min of $y$ is itself changed as do others mentioned in title line.
answered Jan 7, 2018 at 19:05
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$\begingroup$ The place where max/min occurs implies x coordinates, right? $\endgroup$ Jan 7, 2018 at 19:07
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$\begingroup$ Hey, impressed by your answer: math.stackexchange.com/a/1404664/510458 Please tell me which book: Higher algebra or elementary algebra.Tell the chapter too if you remember. $\endgroup$ Jan 7, 2018 at 19:15
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$\begingroup$ Higher Algebra: A Sequel to Elementary Algebra for Schools Henry Sinclair Hall, Samuel Ratcliffe Knight; In India, standard algebra text in colleges for long time. $\endgroup$ Jan 7, 2018 at 19:33
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