dude, not everybody who is or may be asian wants to be called "asian" You don't just go up to David Copperfield and say "look at that white magician" Just call him magician. Jeezez
@Mr Magic Monkey And by comparing, you are indeed mentioning race. Not everybody wants to be compared. Especially when it involves race. Learn how to take into account of others feelings.
Thank you so much this helped a ton participated the most today after only one video. This took away so much stress and clarified so much. Thank you for doing this
I like that he doesn't plot f and f' on the same coordinate plane as it is often done. It's a bad habit. Just imagine that x is time and y=f(x) is the location, then f' is the velocity. The units for the y-axis don't match!
Can someone explain why we would want to graph the derivative? Derivative is slope...why graph that when you can see the slope on the original function?
I am lost here. The original graph had two extrema, which implies that it is a cubic (third degree equation). So, the derivative should be quadratic (second degree) by the power rule. That was all correct but somewhere in there the extrema on the original function f(x) became equal to the extrema on f''(x). At the end of the video, there were three extrema on both the original function and its derivative function. Am I missing something?
Someone correct me if I'm wrong but is it because f(x) has an assymptote? Because if f(x) didn't have that assymptote, f'(x) wouldn't have that 3rd turning point and would continue to go down
because he had added onto the original function; At first there were two, then the derivative had one. He then added another graph onto it which makes it look like one whole graph when theyre seperate
Because there are three points of inflection ( aka a point on a function where the curve changes from being concave to convex, or vice versa.) which will result in three turning points for the derivative graph ( because at point of inflection, where the function concaves and then convexes, the tangent at these points on the function decreases and increases respectively) , whereas the turning points ( aka stationary points ) on the function will be the x- intercept on the derivative graph because at stationary points, dy/dx = 0
@Omar Doudar The only stupid person here is you. The degree of a derivate is one less than the degree of the original function; and, inflection points also depend on degree-a function of degree 3 has 2 turning points for example. Which means that, if we take a function with degree 4, it's derivative should have degree 3 and should have 3-1 turning points.
I'm starting to hate Pr's: one will explain something that the other didn't explain while leaving out something the other did. Why not just give a comprehensive explanation? Like for instance, how do you determine that the point in the middle of the decreasing portion of f is going to be our inflection point in the derivative? Are we just supposed to fly with that?
Good video. The only thing you have to correct is that the y-axis is not the f(x). The latter represents the values of the function, the former is the axis.
