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C3 Product rule

Hey guys, please help with this:

Find the x co-ordinates of the stationary points of -
y=(x^2 + 3)(sqrt(x+2))

thank you!
Reply 1
Avatar for TenOfThem
TenOfThem
18
Original post by AK.tsr
Hey guys, please help with this:

Find the x co-ordinates of the stationary points of -
y=(x^2 + 3)(sqrt(x+2))

thank you!


differentiate (using the product rule)

set = to 0
Reply 2
Avatar for AK.tsr
AK.tsr
OP
1
yes i realise you have to = 0,
can you demonstrate how you do it? that will make it easy for me to see where i went wrong
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by AK.tsr
yes i realise you have to = 0,
can you demonstrate how you do it? that will make it easy for me to see where i went wrong


which bracket are you unable to differentiate?
Original post by AK.tsr
yes i realise you have to = 0,
can you demonstrate how you do it? that will make it easy for me to see where i went wrong

when y=uv
dydx=v∗dudx+u∗dvdx\frac{dy}{dx}=v*\frac{du}{dx}+u*\frac{dv}{dx}
That's the product rule, where u and v are functions.
(edited 11 years ago)
Reply 5
Avatar for davros
davros
16
Original post by reubenkinara
when y=uv
dydx=v∗dydt+u∗dtdx\frac{dy}{dx}=v*\frac{dy}{dt}+u*\frac{dt}{dx}
That's the product rule, where u and v are functions.


Where did t come from? You've messed up some variables there!
Reply 6
Avatar for AK.tsr
AK.tsr
OP
1
Original post by TenOfThem
which bracket are you unable to differentiate?


alright, since you ask this is what i got:

dy/dx = 0.5x^2 + 1.5(x+2)^-0.5 + 2x(x+2)^0.5

when i try and find the solution i think i messed up somewhere
Reply 7
Avatar for TenOfThem
TenOfThem
18
Original post by AK.tsr
alright, since you ask this is what i got:

dy/dx = (0.5x^2 + 1.5)(x+2)^-0.5 + 2x(x+2)^0.5

when i try and find the solution i think i messed up somewhere


that is fine with the brackets
Original post by davros
Where did t come from? You've messed up some variables there!

My honest mistake. Got mixed up with the chain rule.
Reply 9
Avatar for Dalek1099
Dalek1099
21
Original post by AK.tsr
Hey guys, please help with this:

Find the x co-ordinates of the stationary points of -
y=(x^2 + 3)(sqrt(x+2))

thank you!


I'm not going to give you the solution just some handing hints:
the product rule is just (the derivative of the 1st term*the 2nd term)+ (the derivative of the 2nd term*the 1st term) eg.you can prove the derivative of x^2=2x using the two terms are (x)(x) derivative of x=1 1*x=x and the derivative of the other x=1 1*x=x x+x=2x.

Another handy tip is to make it equal zero, to find stationary points and to simplify and solve the algebraic expression as you normally would.
Original post by AK.tsr
alright, since you ask this is what i got:

dy/dx = 0.5x^2 + 1.5(x+2)^-0.5 + 2x(x+2)^0.5

when i try and find the solution i think i messed up somewhere

10ofthem's corrected your missing bracket but If I were you O'd tidy it up a bit by factorizing b4 solving.
Reply 11
Avatar for AK.tsr
AK.tsr
OP
1
Original post by TenOfThem
that is fine with the brackets


thank you! that helped a lot. so i ended up dividing the (x+2)^-0.5 term throughout and that simplified it. cheers big ears!
Reply 12
Avatar for AK.tsr
AK.tsr
OP
1
do you guys know why i left out the brackets? i don't... :P
Original post by AK.tsr
thank you! that helped a lot. so i ended up dividing the (x+2)^-0.5 term throughout and that simplified it. cheers big ears!


:biggrin:
Reply 14
Avatar for AK.tsr
AK.tsr
OP
1
just to clarify the stationary points are -1 and -3. those are right, right?
Reply 15
Avatar for AK.tsr
AK.tsr
OP
1
i'm a bit worried because the book says the stationary points are -1 and -3/5.
i am using an old copy of the main aqa textbook, so i'm pretty sure some of the answers in the back are wrong.
Original post by AK.tsr
...


Looks like the book is right to me

I have no idea what your approach to the solution was but

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