Intergration & Differentiation Question


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Hi guys, I'm suck on a question, and I thought some of you might be able to help:

Find DY/DX of y=5x(4)-x(5)

(4) means power 4 etc.

ok well I got DY/DX of 20x(3)-5x(4) using nx(n-1)

Now it asks me to calculate the co-ordinates of the sationary points. So since gratiants of sationary points always are Zero I set DY/DX to Zero.

=> 20x(3)-5x(4)=0

Now i'm convinced that I have to factorise this to give me my X co-ordinates... but I can't seem to factorise it, can anyone help? There's allot more to this question, but I think I can do the rest by myself after this, I just need some help here. Thanks.

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ok, i only read about the factoring, not the rest of it.

20x^3 - 5x^4 = 0

divide by 5

4x^3 - x^4 = 0

factor out x^3

x^3(4 - x) = 0

so x^3 = 0 (triple root), 4 - x = 0

x = 0, x = 4

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Excellent thanks, I'm hopeless at factorising... I can do all the other stuff but not the factorising :( It's something I'll have to learn ;) Thanks!

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