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# c4 differentiating implicit function questions watch

1. Can anyone help me?

The equation is x^3+y^3=3xy
It is said that find the stationary values and determine whether they are maxima or minima.

I differentiate it fist and get dy/dx=(y-x^2)/(y^2-x)

and then get dy/dx=0 and y-x^2=0. So y=x^2

I have already find out the stationary points (0,0) and (cube root of 2, cube root of 4) .

(cube root of 2, cube root of 4 )is a maximum point if I substitute is into the second derivative.

However, At point (0,0) the second derivative of the function =0 then how do I know whether it is a maxima or minima?

Thanks a lot!!
2. (Original post by pepperzealot)
Can anyone help me?

The equation is x^3+y^3=3xy
It is said that find the stationary values and determine whether they are maxima or minima.

I differentiate it fist and get dy/dx=(y-x^2)/(y^2-x)

and then get dy/dx=0 and y-x^2=0. So y=x^2

I have already find out the stationary points (0,0) and (cube root of 2, cube root of 4) .

(cube root of 2, cube root of 4 )is a maximum point if I substitute is into the second derivative.

However, At point (0,0) the second derivative of the function =0 then how do I know whether it is a maxima or minima?

Thanks a lot!!
try
f'(-0.1) and f'(0.1)
3. (Original post by pepperzealot)
Can anyone help me?

The equation is x^3+y^3=3xy
It is said that find the stationary values and determine whether they are maxima or minima.

I differentiate it fist and get dy/dx=(y-x^2)/(y^2-x)

and then get dy/dx=0 and y-x^2=0. So y=x^2

I have already find out the stationary points (0,0) and (cube root of 2, cube root of 4) .

(cube root of 2, cube root of 4 )is a maximum point if I substitute is into the second derivative.

However, At point (0,0) the second derivative of the function =0 then how do I know whether it is a maxima or minima?

Thanks a lot!!
Are you sure that (0,0) is a stationary point?

I'm not saying you're wrong, but it looks from what you've calculated that dy/dx is undefined at (0,0) so it may need special consideration!
4. (Original post by TeeEm)
try
f'(-0.1) and f'(0.1)
I have tried. But the value of y is also needed to find dy/dx. If I substitute x=0.1to the original equation to get the value of y, there will be three values of y for x=0.1..... It is really complicated!
5. (Original post by davros)
Are you sure that (0,0) is a stationary point?

I'm not saying you're wrong, but it looks from what you've calculated that dy/dx is undefined at (0,0) so it may need special consideration!

Yeah I think it is a correct value.... Actually there are two parts of this question. The first part is just find the x coordinates of the stationary points. I have just checked with the answer at the back of the book. It is said that their x coordinates are 0 and cube root2.. But the second part of the question there is no explanationT T
6. (Original post by pepperzealot)
I have tried. But the value of y is also needed to find dy/dx. If I substitute x=0.1to the original equation to get the value of y, there will be three values of y for x=0.1..... It is really complicated!
let me tell you about this question because I did not pay much attention the first time

this curve is the folium of Descartes and there is a node at the origin which complicates things.

Are you an A level student or undergrad before I continue?
7. both the first and second derivatives are undefined at (0,0)
8. (Original post by TeeEm)
let me tell you about this question because I did not pay much attention the first time

this curve is the folium of Descartes and there is a node at the origin which complicates things.

Are you an A level student or undergrad before I continue?
Thank you very much I am an AS student...
9. (Original post by pepperzealot)
Thank you very much I am an AS student...
Then I can assure you do not need to know how to do this at no board at A level or Further maths.

I remember a recent question on MEI C3 paper where this came up, they drew the graph to show you you were looking for a local max, so you could ignore the origin

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