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# Differentiation watch

1. Find the x-coordinates of the stationary points on the graph of y=3x^3+1/9x
2. (Original post by bronziestone)
Find the x-coordinates of the stationary points on the graph of y=3x^3+1/9x
presumably you have been taught how to differentiate, so differentiate it and since the gradient = 0 for a stationary point, solve dy/dx=0
3. Please check my working as I did this on a train on my phones whiteboard!

You should end up after differentiating and simplyfing with

x^4 -1 =0

This will give you two solutions x=1 and x=-1. I nearly missed the negative. You should really plot this to confirm, plenty of free resources online will tell you if you are right.

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4. Whenever asked to solve for stationary points always differentiate, then let dy/dx=0 and solve for x. The reason for this is that the gradient is 0 at a stationary point.
5. (Original post by Matthew Thomas)
Please check my working as I did this on a train on my phones whiteboard!

You should end up after differentiating and simplyfing with

x^4 -1 =0

This will give you two solutions x=1 and x=-1. I nearly missed the negative. You should really plot this to confirm, plenty of free resources online will tell you if you are right.

Posted from TSR Mobile
The original equation is ambiguously written { 1/(9x) or (1/9)x }, your results may not be correct (I suspect the OP meant 1/(9x) ).
6. (Original post by gdunne42)
The original equation is ambiguously written { 1/(9x) or (1/9)x }, your results may not be correct (I suspect the OP meant 1/(9x) ).
I considered this when i answered and solved for 1/(9x). I found (1/9)x gave non real solutions for x that are i/9 and -i/9. Perhaps we should allow OP to clarify.

(Again please check my solutions. Still on a train and its notso easy without a pen and paper)
7. (Original post by Matthew Thomas)
I considered this when i answered and solved for 1/(9x). I found (1/9)x gave non real solutions for x that are i/9 and -i/9. Perhaps we should allow OP to clarify.

(Again please check my solutions. Still on a train and its notso easy without a pen and paper)
In which case I don't think your solutions are correct

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8. (Original post by gdunne42)
In which case I don't think your solutions are correct

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Wow, you're right. I managed to truly butcher that on the train. :L
Back in the office with a pen and paper, solutions attached.
Attached Images
9. img003.pdf (402.5 KB, 45 views)
10. Thanks😄

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Updated: April 25, 2016
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