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Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

How to estimate a derivative from a graph

How to estimate a derivative from a graph for this example :-

Q ) this graph :

the solution  of it's derivative  is :-

how did it calculated ?

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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: 10,640

Re: How to estimate a derivative from a graph

By looking at the curve I can see it goes through (1,3) , (3,-1) and (-1,-1). 

I'm assuming it is a quadratic as the gradient graph is a straight line.

Substituting these into y = ax^2 + bx + c and solving for a, b and c you'll get:

y = -x^2 +2x +2.  You can check this with a function grapher.

so dy/dx = -2x + 2

So the equation of the gradient graph is y = -2x + 2 as your second graph shows.

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

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: How to estimate a derivative from a graph

how did you assume c=2 , b = 2 , and a = -1?

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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: 10,640

Re: How to estimate a derivative from a graph

The curve  goes through (1,3) , (3,-1) and (-1,-1). 

Substituting these into y = ax^2 + bx + c  you get

3  = a + b + c                                (1)
-1 = 9x^2 + 3b + c                        (2)
-1 = a -b + c                                  (3)

If you subtract (2) from (1) you'll eliminate c
Repeat subtracting (3) from (1)

So you've got a pair of simultaneous equations and can work out a and b, thence c

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

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: How to estimate a derivative from a graph

I didn't understand
how did you exactly calculate these
isn't -1 = a -b + c                                  (3)  should be -1 = - a -b + c                                  (3)
I mean the a is negative ? because you put -1

and what if it was not quadratic  functions what you gonna do?
like :-

sol :

image upload

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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: 10,640

Re: How to estimate a derivative from a graph

When x = -1 is substituted into the quadratic formula the 'a' term is ax^2 = a times -1 times -1.  So the minus signs cancel out.

If the equation isn't a quadratic then what happens next depends on what you know about the formula.  If for example you know it's a cubic then you'd have to start with

y = ax^3 + bx^2 + cx + d.

You could only find all four (a,b,c and d) if you know four sets of coordinates. 

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