Thank you. Good lecture. I wonder about your graph of F. I suppose in (2,3) interval graph should be concave up and from 3 to 5 (3,5) interval the graph of F should be concave down according to the information of derivative. Am I correct?
Yes, Pranav is correct: this video is incorrect and one of the errors is the concavity on (2,3). Another error is the concavity on (3,5) (it should also be concave down). Other errors are that F must be differentiable (so "smooth and curvy" not "sharp and pointy") at both 2 and 3 since f=F' exists at those values but the graph drawn in the video is nondifferentiable at 2 and 3. More specifically, since f(3)=0, the slope of F should be 0 at 3.
4 minutes of explaning taught me more than my professor spending an hour explaining, thank you so much.
You have a great way of explaining! Thank you for the video!
Your handwriting is so gorgeous. Best I've ever seen.
Thank you. Good lecture. I wonder about your graph of F. I suppose in (2,3) interval graph should be concave up and from 3 to 5 (3,5) interval the graph of F should be concave down according to the information of derivative. Am I correct?
Shouldn't the graph between (2,3) be concave down since F'(x) is decreasing
Yes, Pranav is correct: this video is incorrect and one of the errors is the concavity on (2,3). Another error is the concavity on (3,5) (it should also be concave down). Other errors are that F must be differentiable (so "smooth and curvy" not "sharp and pointy") at both 2 and 3 since f=F' exists at those values but the graph drawn in the video is nondifferentiable at 2 and 3. More specifically, since f(3)=0, the slope of F should be 0 at 3.
Here's my version of this video: ua-cam.com/video/Zz8mE0RtO78/v-deo.html.
you're a god
very helpful, thanks
Good vid
thank you
Wonder what happened to this dude.
One year after your comment, I came across this guy and wondered the same
@@baolongnguyen7844Almost 1 year later, I am wondering the same