neptune
Member
Hello everyone,
The derivative of function
is
, what i understood is if function
represents the graph of time and displacement, its derivative at a point on graph tells me the instantaneous velocity.
Question 1: since we find derivative by making the
as small as we can lim->0 but we never make it a point, so why do we call it derivative at a point ? or instantaneous velocity at a point. it better be called velocity as x approaches at that particular point.
If
represents the area of square its derivative
represents change in area when side is changed by small amount. but when i put in numbers in
it just tells me the area at that particular point.
Question 2: if it tells me the area of square at particular point where is the notion of change coming in ?
and it is not accurate as it ignores the
part, i could have found out the area of square much more accurately by simply putting the value in the function.
The derivative of function
![32f5240d0dbf2ccbe75ef7f8ef2015e0-2.png](https://www.electro-tech-online.com/latex-editor/pics/32f5240d0dbf2ccbe75ef7f8ef2015e0-2.png)
![2204c2b4d60ae2fd5279ec54cfaed2a4-2.png](https://www.electro-tech-online.com/latex-editor/pics/2204c2b4d60ae2fd5279ec54cfaed2a4-2.png)
![32f5240d0dbf2ccbe75ef7f8ef2015e0-2.png](https://www.electro-tech-online.com/latex-editor/pics/32f5240d0dbf2ccbe75ef7f8ef2015e0-2.png)
Question 1: since we find derivative by making the
![acd2b09d39705a84bff035c18c9faea9-2.png](https://www.electro-tech-online.com/latex-editor/pics/acd2b09d39705a84bff035c18c9faea9-2.png)
If
![32f5240d0dbf2ccbe75ef7f8ef2015e0-2.png](https://www.electro-tech-online.com/latex-editor/pics/32f5240d0dbf2ccbe75ef7f8ef2015e0-2.png)
![0665296487cc2301b531238d6c01fb17-2.png](https://www.electro-tech-online.com/latex-editor/pics/0665296487cc2301b531238d6c01fb17-2.png)
![2204c2b4d60ae2fd5279ec54cfaed2a4-2.png](https://www.electro-tech-online.com/latex-editor/pics/2204c2b4d60ae2fd5279ec54cfaed2a4-2.png)
Question 2: if it tells me the area of square at particular point where is the notion of change coming in ?
and it is not accurate as it ignores the
![1dbb91980dff3422a3ed6ba9ce08a013-2.png](https://www.electro-tech-online.com/latex-editor/pics/1dbb91980dff3422a3ed6ba9ce08a013-2.png)