# differentiation

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#2

(Original post by

find the stationary points of :

**limitlesspuffy**)find the stationary points of :

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(Original post by

What happens when you try the usual approach? Is there a particular point that you are stuck at?

**Pangol**)What happens when you try the usual approach? Is there a particular point that you are stuck at?

It is 15x^1/4 -5/9x

Then you set that to 0 and solve.

I've got 135x^1/4 -5x=0 so far

and idk how to solve after that

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#4

(Original post by

so dy/dx i've worked out

It is 15x^1/4 -5/9x

Then you set that to 0 and solve.

I've got 135x^1/4 -5x=0 so far

and idk how to solve after that

**limitlesspuffy**)so dy/dx i've worked out

It is 15x^1/4 -5/9x

Then you set that to 0 and solve.

I've got 135x^1/4 -5x=0 so far

and idk how to solve after that

^{1/4}and see where that takes you.

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^{1/4}(135-5x

^{4})=0

So x=0 and 135-5x

^{4}=0

so x

^{4}=27

x=2.2795 (4 d.p)

I feel like this is wrong.

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#6

(Original post by

x

So x=0 and 135-5x

so x

x=2.2795 (4 d.p)

I feel like this is wrong.

**limitlesspuffy**)x

^{1/4}(135-5x^{4})=0So x=0 and 135-5x

^{4}=0so x

^{4}=27x=2.2795 (4 d.p)

I feel like this is wrong.

^{1/4})(x

^{4})?

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(Original post by

I wouldn't bother multiplying by 9, that can come later. It is the power that is attached to the x in the bracket that needs looking at. If you multiply out your factorisation, do you get back where you started? What is (x

**Pangol**)I wouldn't bother multiplying by 9, that can come later. It is the power that is attached to the x in the bracket that needs looking at. If you multiply out your factorisation, do you get back where you started? What is (x

^{1/4})(x^{4})?^{1/4})(x

^{4})=x

^{1}so it is what i started with

so if i don't multiply by 9, I get 15 - 5/9x

^{4 }=0

Then I still get x

^{4}=27

oh wait in (x1/4)(x4), do you add 1/4 and 4

Last edited by limitlesspuffy; 1 month ago

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#8

(Original post by

(x

so if i don't multiply by 9, I get 15 - 5/9x

Then I still get x

oh wait in (x1/4)(x4), do you add 1/4 and 4

**limitlesspuffy**)(x

^{1/4})(x^{4})=x^{1}so it is what i started withso if i don't multiply by 9, I get 15 - 5/9x

^{4 }=0Then I still get x

^{4}=27oh wait in (x1/4)(x4), do you add 1/4 and 4

Last edited by Pangol; 1 month ago

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(Original post by

You do indeed add them.

**Pangol**)You do indeed add them.

Is x=0 also a solution?

Which means can x

^{1/4}=0 since 0

^{1/4}=0

Last edited by limitlesspuffy; 1 month ago

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#10

x = 0 is a solution of dy/dx = 0, but look again at the equation as given to you in the question to see if this counts.

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(Original post by

x = 81 is correct. Note that the question asks for the stationary points, so you will have to provide a coordinate, not just an x-value.

x = 0 is a solution of dy/dx = 0, but look again at the equation as given to you in the question to see if this counts.

**Pangol**)x = 81 is correct. Note that the question asks for the stationary points, so you will have to provide a coordinate, not just an x-value.

x = 0 is a solution of dy/dx = 0, but look again at the equation as given to you in the question to see if this counts.

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#12

if y=12x^5/4-5/18x^2-1000 then dy/dx = 15x^1/4-5/9x

we then know that 15x^1/4 = 5/9x

then divide both sides by x so 15x^-3/4 = 5/9

multiply both sides by 15 so x^-3/4 = 1/27

therefore 1/x^3/4 = 1/27 so x^3/4 must be equal to 27

x^3/4 = the fourth root of x^3 so that = 27

cube root both sides: fourth root of x = 3

both sides to the fourth power and x = 81 which is the only value for x

then substitute that into the original equation for y to get the point

we then know that 15x^1/4 = 5/9x

then divide both sides by x so 15x^-3/4 = 5/9

multiply both sides by 15 so x^-3/4 = 1/27

therefore 1/x^3/4 = 1/27 so x^3/4 must be equal to 27

x^3/4 = the fourth root of x^3 so that = 27

cube root both sides: fourth root of x = 3

both sides to the fourth power and x = 81 which is the only value for x

then substitute that into the original equation for y to get the point

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#13

(Original post by

if y=12x^5/4-5/18x^2-1000 then dy/dx = 15x^1/4-5/9x

we then know that 15x^1/4 = 5/9x

then divide both sides by x so 15x^-3/4 = 5/9

multiply both sides by 15 so x^-3/4 = 1/27

therefore 1/x^3/4 = 1/27 so x^3/4 must be equal to 27

x^3/4 = the fourth root of x^3 so that = 27

cube root both sides: fourth root of x = 3

both sides to the fourth power and x = 81 which is the only value for x

then substitute that into the original equation for y to get the point

**NMB27**)if y=12x^5/4-5/18x^2-1000 then dy/dx = 15x^1/4-5/9x

we then know that 15x^1/4 = 5/9x

then divide both sides by x so 15x^-3/4 = 5/9

multiply both sides by 15 so x^-3/4 = 1/27

therefore 1/x^3/4 = 1/27 so x^3/4 must be equal to 27

x^3/4 = the fourth root of x^3 so that = 27

cube root both sides: fourth root of x = 3

both sides to the fourth power and x = 81 which is the only value for x

then substitute that into the original equation for y to get the point

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