In the lecture videos I have noticed that Dr. Ng, refers to the derivative as being the slope of a function at a particular point, am I missing something? Hate to think that my understanding of math is sufficient to question what he is saying- what I remember from over a decade ago of my calculus course, a derivative is the slope of the tangent of a function at a particular point.
Can someone please help clarify this point?
Thanks in advance,
You’re right that the definition of the slope of a curve is the slope of the tangent at that point on the curve. What Prof Ng says just assumes you know that definition. What else would he mean by “slope”?
Well, if you want to “full pedantic” here, actually “the derivative” is a function, which gives the slope of the curve at each point in the domain of the original function, right?
From my perspective, both of them refer to the same thing. Geometrically, the slope of the tangent of a curve at a particular point, for example A, is \tan A (The illustration is in the image below). On the other hand, \tan A = \frac{\Delta y}{\Delta x}, and when you take \Delta x \to 0 (very very close to 0), it’ll become the definition of derivative of the function at that point. Hope you get what I’ve written here.
@sonnh1902, thank you for the explanation. I have deleted my previous post, for I was incorrect. I think that I now understand- the point that I was hung up on was evidently a point that I was reading and understood, but was not applying in my thinking- that the slope changes and it’s specific to a particular point on the function, applying that made it abundantly clear that the two are the same.
Also, thanks @paulinpaloalto!
