Question

why do we equate dy/dx = 0 ? is it to find the coordinates of the gradient / max. or min. points?

Answer 1

Lets think of it geometrically. dy/dx=0 means slope of tangent at that point=0. What does that mean? It means the point is either a maxima or minima:

Answer 2

dy/dx is not 0 .... is just represent a very very small; value that is insignificant in an overall equation.

Answer 3

hmm, i was reading the question differently lol

Answer 4

dx/dy is the slope of the tangent line. When it is 0, the tangent line is horizontal. This can happen in three situations: the point is a local minimum, the point is a local maximum, or the point is an inflection point. To be sure what the point is, the second derivative is helpful.

Answer 5

we set dy/dx = 0 because we wish to find where slope is horizontal. Unless you meant to ask why do we set dy/dx = 0 when we want to find max/min, then it's different question

Answer 6

Remember way back in algebra when they said y=mx+b and they said m is the slope? What's slope? Remember, it's just rise over run.

Rise is really just the movement in the y direction
run is a cute way of saying movement in the x direction.

So how much do we move in any direction? Just take any two points and subtract one from the other. For instance if you move from 4 to 7 then how far did you move? Well 7-4=3 which makes sense right? We just moved 3 points to get from 4 to 7. In math terms we would just say \[\Large x_{final}-x_{initial}\] or maybe you saw it written as \[\Large x_2-x_1 \ \ \ \ \ or \ \ \ \ \ x_f-x_i\]

It doesn't really matter but you probably saw it written as \[\Large \frac{y_2-y_1}{x_2-x_1}=m\] Right? That's all the slope is in algebra.

But now we're coming along and saying that \[\Large x_2-x_1= \Delta x\] The triangle thingy is called "Delta" and all it means is change in x. It's just a shortcut to writing out this little simple subtraction equation thing. There's really nothing mystical going on here, except some dudes were lazy and decided this triangle looked much cooler than writing subtraction between two points to find the distance.

So now we can see that we can rewrite our slope m as \[\Large \frac{\Delta y}{\Delta x}=m\] Now in calculus we are looking at things that aren't lines, so at any point on the graph the slope is different. Lines were simple and m was a constant no matter where you were. So now we have to consider that at any point x, the slope could be different. So they use this fancier notation where they turn Delta into a "d" and it looks like this: \[\Large \frac{dy}{dx}\] and that's the slope. Now you might wonder why they changed it. Well the problem is because in order to find the slope we're basically saying that the distance between x2 and x1 is zero. So in a way we're saying there's no distance between the points to find the slope at an exact location. Seems weird, and it is. But that's what the limit is saying. It's just the slope formula in disguise! \[\Large \frac{dy}{dx}=\lim_{h \rightarrow 0} \frac{ f(x+h)-f(x)}{(x+h)-x}\] See how this is just a fancy version of the slope formula?

I hope that helps a little.

Answer 7

thanks for all the help ! really appreciate it!

Answer 8

Cool, if you have any more questions I'll help you out. Calculus is definitely something that "makes sense" it just is usually a hard subject to teach and hard to understand until you think about some things long enough. After all, it wouldn't be used by scientists everywhere to make cool stuff like computers and rocket ships if it didn't make sense! =D

Answer 9

You also apply some common sense,
derivative is slope
So when a slope is 0 when their is flat line


By Slope i mean it is not going either up or down it is flat
so slope is 0

derivative = slope
When slope 0
dy/dx =0