Two things: 1)Before finding critical numbers, I strongly recomend finding the domain first! 2) the only way for a quotient to be 0 is if the numerator is 0. No weird rule about that
Shouldn't you also be solving for the values for which g'(y) doesn't exist on the real number line? Functions like f(x) = |x| have a max or min at points like that
There are no real values at which (y²-y+1)²=0 (as the discriminant for y²-y+1=-3, meaning there are no real values in which the function is equal to 0, and the only number which when squared outputs 0 is 0), so there are no values at which g'(y) doesn't exist.
Hey Mr. Blackpenredpen. i was watching your trig and hyp function derivative videos , but i couldn't find your inverse hyp function video . Am i blind or you havn't made the video ?
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 🥺🙏.
Doesn't the term "critical values" or "critical numbers" also include values for which the 2nd derivative is zero? I think they're called points of inflection. I am an analytic geometry hobbyist and love working with 1st and 2nd derivatives (and sometimes higher ones).
nope thats an entirely separate concept and not all points where the second derivative is zero are inflection points as an inflection point is where a graph changes concavity and a zero in the second derivative does mean that it could have an inflection there but it does not mean there is for certain
@@rslitman Points of inflection are points where the 2nd derivative equals zero, which is unrelated to the denominator equaling zero. Points where the denominator equals zero, are of interest to optimization problems, and depending on who you ask, these may or may not be critical numbers.. There are several different kinds of behaviors that a denominator of zero could imply: 1. A hole, or removable singularity, where the numerator also coincidentally equals zero 2. A vertical asymptote, where the function would be undefined. This could also imply that your absolute maximum, or minimum, really approaches infinity at this point, rather than being one of your local maxima where the numerator equals zero. 3. A kink or cusp, where there is an abrupt change in slope. This can cause a local maximum or minimum, without also being a stationary point.
Two things:
1)Before finding critical numbers, I strongly recomend finding the domain first!
2) the only way for a quotient to be 0 is if the numerator is 0. No weird rule about that
Nice point there, be sure to use parenthesis when you have more than one term
Thanks for the reminder
Shouldn't you also be solving for the values for which g'(y) doesn't exist on the real number line? Functions like f(x) = |x| have a max or min at points like that
There are no real values at which (y²-y+1)²=0 (as the discriminant for y²-y+1=-3, meaning there are no real values in which the function is equal to 0, and the only number which when squared outputs 0 is 0), so there are no values at which g'(y) doesn't exist.
@@estebson That's true, I didn't realize that.
This video is 2 years ago but still very helpful for me.
thanks so much
Hey Mr. Blackpenredpen. i was watching your trig and hyp function derivative videos , but i couldn't find your inverse hyp function video . Am i blind or you havn't made the video ?
i keep getting distracted by the pokeball
Could you please bring series on contunuity and differentiability
It will help a lot .
Ita a request
I feel like that would belong better on the main channel
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 🥺🙏.
Sorry but it was the switching of markers for me😂
Doesn't the term "critical values" or "critical numbers" also include values for which the 2nd derivative is zero? I think they're called points of inflection. I am an analytic geometry hobbyist and love working with 1st and 2nd derivatives (and sometimes higher ones).
nope thats an entirely separate concept and not all points where the second derivative is zero are inflection points as an inflection point is where a graph changes concavity and a zero in the second derivative does mean that it could have an inflection there but it does not mean there is for certain
@@radiationgaming889 Thanks for the clarification. It has been a long time since I studied calculus.
@@rslitman no problem also think that a linear graph would have no points of inflection despite the second derivative always being zero
@@rslitman Points of inflection are points where the 2nd derivative equals zero, which is unrelated to the denominator equaling zero.
Points where the denominator equals zero, are of interest to optimization problems, and depending on who you ask, these may or may not be critical numbers.. There are several different kinds of behaviors that a denominator of zero could imply:
1. A hole, or removable singularity, where the numerator also coincidentally equals zero
2. A vertical asymptote, where the function would be undefined. This could also imply that your absolute maximum, or minimum, really approaches infinity at this point, rather than being one of your local maxima where the numerator equals zero.
3. A kink or cusp, where there is an abrupt change in slope. This can cause a local maximum or minimum, without also being a stationary point.