critical numbers of an absolute value of a function (with quadratic inside)

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Calculus 1: critical numbers of an absolute value of the function (with quadratic inside)

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I am not first
I am not last
But when bprp posts
I do click fast

antonlindemer

Generally speaking, for an arbitrary polynomial p(x), the first derivative of |p(x)| is [|p(x)|/p(x)] p'(x), so any point x such that p(x) = 0 will be not differentiable if such x does not make p'(x) = 0. Nevertheless, if x satisfies both conditions p(x) = 0 and p'(x) = 0, we get x has a winding number >= 2, a.k.a. a repeated root of p(x), then by the limit definition, we get that the first derivative of |p(x)| at x is 0 regardless which approach we use, and graphically we can see that the polynomial is smooth at such x value. (It is easier to visualize that if we keep both the domain and the codomain in the real set although it still holds by bringing both into the complex world.) But again, regardless of whether the roots of |p(x)| are differentiable, we should always keep in mind that all those roots are relative minimum (a.k.a. local minimum) since |p(x)| >= 0 provided that there is no other x value in the domain around the roots giving us |p(x)| < 0.

kobethebeefinmathworld

So d/dx (ax² - bx + c ) taking the deratives ( 2ax - b ) = 0
2ax = b
X = b/2a? ( Turning point)???

jx_was_here

Hella helpful, abs values are very simple in theory but when it comes down to solving problems with it it gets complicated fast

piupolino

Can I do d/dx |x| = x/|x| ??
Are there any advantages to put the absolute value in the numerator?

Drestanto

Which value of n
1 to ∞ ∫ ( {x} / (x)^(n+1) ) dx question solution is =( 1/(n+1) )
Where {x} = ( x - floor(x) )
Please make a video on this question 🥺🙏.

numberandfacts

He’s growing impatient with the slow students in this video

robberbarron

evaluate: integration 2^(2^(2^x)) * 2^(2^x) * 2^x dx
This question is very hard 👆👆
you will never be able to solve

balkrishna

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