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C3 Chain Rule

Came across this question and my solution is different from the textbook answer.
The curve C is defined by the equation:

y=4x2+12(1−x)2y = \dfrac{4}{x^2} + \dfrac{1}{2(1-x)^2}

Show that there is only one stationary point and find its coordinates.

I used chain rule then found dy/dx to be:

(1−x)−3−8x−3 (1-x)^{-3} - 8x^{-3}

When I set this equal to 0 I proved there was one stationary point but my x-coordinate was 1/3 when the book had 2/3.

Where have I went wrong?
Original post by ozmo19
Came across this question and my solution is different from the textbook answer.
The curve C is defined by the equation:

y=4x2+12(1−x)2y = \dfrac{4}{x^2} + \dfrac{1}{2(1-x)^2}

Show that there is only one stationary point and find its coordinates.

I used chain rule then found dy/dx to be:

(1−x)−3−8x−3 (1-x)^{-3} - 8x^{-3}

When I set this equal to 0 I proved there was one stationary point but my x-coordinate was 1/3 when the book had 2/3.

Where have I went wrong?


your dy/dx is fine...

1/( 1 - x ) 3 = 8/(x)3

cube root both sides... 1/( 1 - x ) = 2/(x)

*now rearrange & solve to get the book answer*
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ozmo19
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Original post by the bear
your dy/dx is fine...

1/( 1 - x ) 3 = 8/(x)3

cube root both sides... 1/( 1 - x ) = 2/(x)

*now rearrange & solve to get the book answer*


I had done this but had done
1/( 1 - x ) 3 = 1/8(x)3 by accident.

Thank you!
Original post by ozmo19
I had done this but had done
1/( 1 - x ) 3 = 1/8(x)3 by accident.

Thank you!


we are here to help :h: *
Reply 4
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ozmo19
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Original post by the bear
we are here to help :h: *


Not sure how to go about this one:


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image.jpeg55.5KB
A: it is a product rule with a little bit of chain too...

u = e-x

v = 4e2x - 2ex

remember eax differentiates to aeax...

B: alternatively you could multiply out the brackets then you would not need the product rule ...
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Avatar for ozmo19
ozmo19
OP
16
Original post by the bear
A: it is a product rule with a little bit of chain too...

u = e-x

v = 4e2x - 2ex

remember eax differentiates to aeax...

B: alternatively you could multiply out the brackets then you would not need the product rule ...


Took du/dx as e^-x and not -e^-x - Thanks for the reminder:biggrin:

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