Graph Drawing (1 Viewer)

[wintering]

can someone explain to me how to draw the graph of the first and second derivatives, given the the graph of the function? thanks

 

[tommykins]

You look at the function, turning points make y = 0, inflextion points create a double root.

Also note that the gradient function is always one less degree than the normal function.

 

[Epistemophobia]

I can draw me a pretty mean graph.

 

[lyounamu]

can someone explain to me how to draw the graph of the first and second derivatives, given the the graph of the function? thanks

Learn the difference between them first.

For example:

First derivative is the gradient function with the second derivative being the function that shows the concavity.

Some useful knowledges are:

At the maximum/minimum points of the function, dy/dx = 0
At the maximum/minimum points on the gradient function, second derivative = 0

 

[Epistemophobia]

Thanks

 

[wintering]

Learn the difference between them first.

For example:

First derivative is the gradient function with the second derivative being the function that shows the concavity.

Some useful knowledges are:

At the maximum/minimum points of the function, dy/dx = 0
At the maximum/minimum points on the gradient function, second derivative = 0

i'm aware of all of that. hence the specificity of my question. thanks for trying, though

You look at the function, turning points make y = 0, inflextion points create a double root.

Also note that the gradient function is always one less degree than the normal function.

i'm not sure i get it. double root? one less degree? x_o

 

[henry08]

Also note that the gradient function is always one less degree than the normal function.

Can you please explain this.

 

[henry08]

A double root means it cuts the x-axis twice.

 

[tommykins]

回复: Re: Graph Drawing

Can you please explain this.

Consider f(x) = x^n
f'(x) = nx^n-1

That is, it has n-1 roots whereas x^n has n roots.

As you keep differentiating, the degree decreases by 1, this in turn leads to a decrease in the number of roots.