Differentiation

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

Reply 2

Matthew Thomas

Please check my working as I did this on a train on my phones whiteboard! :biggrin:

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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Reply 3

liamb80

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.

Reply 4

gdunne42

Original post by Matthew Thomas

Please check my working as I did this on a train on my phones whiteboard! :biggrin:

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) ).

(edited 8 years ago)

Reply 5

Matthew Thomas

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)