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C3 Applications of Differentiation

c3 2f.jpgI am stuck on Q3,4,6,7,8,9,10,11 of the questions could anyone help? I have done Q1,2 &5.
(edited 7 years ago)
Reply 1
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B_9710
18
What exactly is it that you are unable to do?
Reply 2
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henb99
Finding the coordinates mainly (found my old account hence the different username)
Original post by henb99
Finding the coordinates mainly (found my old account hence the different username)

Original post by henbnyc
I am stuck on Q3,4,6,7,8,9,10,11 of the questions could anyone help? I have done Q1,2 &5.


Q3 - I can't see what gradient the book shows to I'll just refer to it as mm. Anyway, you have y=x1+xy=\frac{x}{1+x} so you need to find dydx\frac{dy}{dx} by using an appropriate differentiation rule that you should know. Set dydx=m\frac{dy}{dx}=m and solve for xx to see at what x coordinates the gradient is mm.

Once you have your value(s) of xx, plug them back through y=x1+xy=\frac{x}{1+x} to find your y coordinates.
Reply 4
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B_9710
18
Original post by henb99
Finding the coordinates mainly (found my old account hence the different username)


It may be easier to differentiate x1+x \frac{x}{1+x} if you express it in the form 1−11+x 1-\frac{1}{1+x} .
Reply 5
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Aklaol
12


How do I solve? ^ :frown:
Original post by Aklaol


How do I solve? ^ :frown:


Create your own thread on the Maths forum and ask this. Don't hijack other threads, thanks.
Reply 7
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henb99
Original post by RDKGames
Q3 - I can't see what gradient the book shows to I'll just refer to it as mm. Anyway, you have y=x1+xy=\frac{x}{1+x} so you need to find dydx\frac{dy}{dx} by using an appropriate differentiation rule that you should know. Set dydx=m\frac{dy}{dx}=m and solve for xx to see at what x coordinates the gradient is mm.

Once you have your value(s) of xx, plug them back through y=x1+xy=\frac{x}{1+x} to find your y coordinates.


I have tried this but only get one set of coordinates instead of two

When I differentiate using the quotient rule I get 1/(1+x)^2
Original post by henb99
I have tried this but only get one set of coordinates instead of two

When I differentiate using the quotient rule I get 1/(1+x)^2


That's correct. When it comes to square rooting, you should get 2 solutions because x2=a⇒x=±ax^2=a \Rightarrow x=\pm \sqrt{a}
Reply 9
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henb99
Original post by RDKGames
That's correct. When it comes to square rooting, you should get 2 solutions because x2=a⇒x=±ax^2=a \Rightarrow x=\pm \sqrt{a}


So the gradient 1/9 is equal to 1+x^-2

-8/9=x^-2
Original post by RDKGames
Create your own thread on the Maths forum and ask this. Don't hijack other threads, thanks.


Lmao you look like a killjoy and you sure are :smile:
Original post by henb99
So the gradient 1/9 is equal to 1+x^-2

-8/9=x^-2


Nope. So then 19=(1+x)−2⇒9=(1+x)2⇒±3=1+x\frac{1}{9}=(1+x)^{-2} \Rightarrow 9=(1+x)^2 \Rightarrow \pm 3 = 1+x
Original post by BluntBluster
Lmao you look like a killjoy and you sure are :smile:


Oh definitely a lot of joy posting complicated maths problems on a simple A-Level thread.
Reply 13
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henb99
Original post by RDKGames
Nope. So then 19=(1+x)−2⇒9=(1+x)2⇒±3=1+x\frac{1}{9}=(1+x)^{-2} \Rightarrow 9=(1+x)^2 \Rightarrow \pm 3 = 1+x


Thank you so much I know how dumb I must sound, I have worked it out correctly

For question 4, when I differentiated I got 3x(x+1)^2 which is equal to the gradient 7

after this I got stuck again, there should only be one point (P)
Original post by henb99
Thank you so much I know how dumb I must sound, I have worked it out correctly

For question 4, when I differentiated I got 3x(x+1)^2 which is equal to the gradient 7

after this I got stuck again, there should only be one point (P)


Please state the original function, they are hard to see. Is it y=x(x−1)3y=x(x-1)^3??? If so, check your differential again.
Reply 15
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henb99
Original post by RDKGames
Please state the original function, they are hard to see. Is it y=x(x−1)3y=x(x-1)^3??? If so, check your differential again.


My bad I had a plus instead of a minus
I have got it to be (2,2)
Original post by henb99
My bad I had a plus instead of a minus
I have got it to be (2,2)


Correct.
Original post by RDKGames
Correct.


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