We can model the graph around x1 using the tangent line very well for small enough scales, as we have seen in the linear approximations video. So, if f(x) is continuous around x1 and f'(x1) != 0, the the tangent line at x1 will be higher than f(x1) in one direction, and lower in the other direction. For instance, for a positive derivative, the slope is going to be positive, so the tangent line will take values greater than f(x1) to the right, and lower than f(x1) to the left. But since the tangent line approximates the graph, we then know, that the values of f(x) must also go up to one side of x1, and down to the other side! Obviously, then, x1 is not a local minimum/maximum.
Montage = Awesome. Thanks for your great videos, you rock dude!
this is the only math channel which have zero dislike on more than 90% videos i guess
Math subs are legit the best on UA-cam
Awesome video, cleared some things up, the two questions were spot-on
Thanks so much for these excellent videos!
We can model the graph around x1 using the tangent line very well for small enough scales, as we have seen in the linear approximations video.
So, if f(x) is continuous around x1 and f'(x1) != 0, the the tangent line at x1 will be higher than f(x1) in one direction, and lower in the other direction. For instance, for a positive derivative, the slope is going to be positive, so the tangent line will take values greater than f(x1) to the right, and lower than f(x1) to the left.
But since the tangent line approximates the graph, we then know, that the values of f(x) must also go up to one side of x1, and down to the other side! Obviously, then, x1 is not a local minimum/maximum.
Thanks for these awesome videos !
Thank you so much..
The pausing montage 😂nice one
I laughed so hard at that moment.
@@ian.ambrose +1
Prof are you taching according to the thomas calculus topics
Finding max/min in a function going into infinity is impossible.