# How do the tangents,derivatives,continuity,diffrentiability of a function get affected if the function is squared? [closed]

Please explain graphically the above changes(I imply changes in roots, derivatives at some points, continuity and differentiability at some points etc

• I cannot see a question here. Jan 7, 2018 at 18:52
• I mean any function not very specific, I request you to answer my query using various functions as examples. Jan 7, 2018 at 18:54

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.

• Can this be shown graphically? Jan 7, 2018 at 19:03
• It's pretty easy to graph the function $y=1$ and observe its various properties. Jan 7, 2018 at 19:36

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.

• The place where max/min occurs implies x coordinates, right? Jan 7, 2018 at 19:07
• Yes, x coordinate. Jan 7, 2018 at 19:10
• 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. Jan 7, 2018 at 19:15
• 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. Jan 7, 2018 at 19:33
• Got it.Thankyou. Jan 9, 2018 at 8:20