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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

Hello,

I have been having problems drawing the derivative of a function. What I mean is that just given the graph of some function $f$ and not its definition, you are supposed to draw $f'$. I understand that when the tangent line of the graph is horizontal, this will correspond to $f'(x)=0$, but my question is if I draw all the extrema points how can I know what the rest of graph will look like?

Well, to make this more clear, let's say I give you the graph of $f(x)=x^3-x$ (I give you the graph, but you don't know its actual definition). I can see that the graph changes from going up to down around $x=-0.8$ (I don't know if it's called a max point in English) and the function then changes from going down to up around $x=0.8$ (I don't know if it's called a min point in English) that means I know the two roots of the derivative, but how can i draw the rest of the derivative's graph?

I have been having problems drawing the derivative of a function. What I mean is that just given the graph of some function $f$ and not its definition, you are supposed to draw $f'$. I understand that when the tangent line of the graph is horizontal, this will correspond to $f'(x)=0$, but my question is if I draw all the extrema points how can I know what the rest of graph will look like?

Well, to make this more clear, let's say I give you the graph of $f(x)=x^3-x$ (I give you the graph, but you don't know its actual definition). I can see that the graph changes from going up to down around $x=-0.8$ (I don't know if it's called a max point in English) and the function then changes from going down to up around $x=0.8$ (I don't know if it's called a min point in English) that means I know the two roots of the derivative, but how can i draw the rest of the derivative's graph?

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