Problem with the derivative of piece wise function

RRamanujam shared this question 2 years ago

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I found the derivative of a piecewise function using the command f'. I face two problems

1) In algebra view the derivative is shown as f'(x)=f'(x) only. The actual function is not shown

2) Not able to find the point of intersection of f' with the x axis using intersection tool

Files: piecewise fn.ggb

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Comments (5)

ccambre ● 2 years ago

As you illustrate, you can only calculate the equation of the derivate of a derivable function, where a piece wise function is not derivable in all the points of its domain.

However, you can calculate The two derivates seperately as Derivate(If(x ≤ 2, x²)) and Derivate(If(x>2, 2(x-3)²+2)). This will give you the equations and as well provide you the possibility to find the intersecting points.

chris

Files: piecewise fn.gg...

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RRamanujam ● 2 years ago

OK, the command derivative(f) also gives the equations. But what is the difference between the commands f' and Derivative ?

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mathmagic ● 2 years ago

do not use f' you can to use derivative(f) for the function

bfca756a465787f36715ed7e16c12d75

for functions intersection with xaxis there is roots() command

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RRamanujam ● 2 years ago

It's OK . But what is the difference between the commands f' and derivative. Why does GeoGebra takes them in different manner ?

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Sukesh A ● 2 years ago

In line with this question the following is observed....

If we create a piecewise function using the command If(x<2,2x,2) and intersect the function (in my case f) with xAxis using the command Intersect(f,xAxis) there is no problem at all.

But if the function is created using the command If(x<2,2x,x>=2,2), then the intersection with x Axis is undefined.

Is this the issue with the implementation of the If command in case of multiple conditions?

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