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Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

voltage derivative

Hi please see this question with its solution
I will post three images the first is the question and the second is the solution and finally the last image is my suggested derivative graph I know it's wrong but I want you to direct me
my question is about the derivative ,
why  derivative does not exist where the graph has a corner?
and how the solution setter calculate the  positive and negative segments  in such this way?
my suggested graph ask about why there is positive and negative segments are missing? I colored it in red .. in the third image

sol :

my suggested graph

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: voltage derivative

All derivatives are defined as the limit of the chord gradient between points A and B on the curve as B approaches A.

If the gradient changes instantly to a different value it cannot be determined at that point as the limit is different on one side of the point to the other. 

If you compare the 'official' answer  with yours, you'll see that your lines 'overlap' each other so that, for a given value of x, there are two values of dy/dx.  That cannot be correct.

Here's a written description of what the gradient is 'doing'.

It is positive and constant for a while; then it switches to zero for a while; then it is negative and constant for a while; then zero again; then this four stage description repeats.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob