A-Level C1 differentiation question

Given that

y = 2x^(3/2) - 1,

Show that

4x^2((d^2)y/dx^2) - 3y = k

Heres an image:

https://lh3.googleusercontent.com/JBmxtWLflz0namZUv-5w-Oz4DwaWzpXeTgkYZlvpepKucS_VKwZtqCeM7VEI-4XzUul4bVyZAkQlbR0-NqO1l8Mu9oCZ1DB_aSxnZlL-eQd842QlJfOyTwbyeVsye4PqAY-a8lEPfAanjPfWmxQ4ykPpLApfAvW0NyHI0R1O97oISk3urUdNN8L5xPHOqWSRPRq4oVs7kZhiFWTEmkiUynWwBoXcXfZrDZLrCbIup_YCcm4pO4hnNlwsnp9MbtMYA1SBSqwEV83bZ_dsrDpwd0O-8PXLwvBsoL6rbE8Zzk8e_M9Rc5zGUHahaX-R9djrfk5QEozsT8vgls66dGBZUgxPCoN29b98bgYQBfF1zgPrPqi9ZEYcvDTkoyBLQ-rXEbtRb2JKLYq35QC47EcoWLdjjBLwXWCHCAht8wH6U1NekU3KA_VAeD-UmvktesQhu8wcjbT3vPeyfwBFGerRmPUUd-XLqdLgFsUgNnUgzA2qJycXYY7nprGX2NsmPpMZMi29VZsGs8l9W3FZIn_URt1ViexqUYUVF76rXREDuep3Rf8Y8eNJnEr-qNYlvylhP2-Rj31EozqO5kA6ZQUMcRmFow=w1377-h775-no

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Reply 1

Kevin De Bruyne

Original post by Tobiq

What have you tried? :h:

Reply 2

Tobiq

Original post by SeanFM

What have you tried? :h:

Literally no help whatsoever....

Reply 3

Tobiq

Original post by SeanFM

What have you tried? :h:

Reply 4

lerjj

Original post by Tobiq

Literally no help whatsoever....

Calculate the second derivative, plug everyth into the left hand side of the equation and find out what k is. Unless you show some sign of trying that, there's not much point just telling you the answer.

Reply 5

Kevin De Bruyne

Original post by Tobiq

Literally no help whatsoever....

I'm sorry. :redface:

good luck with your question :h:

Reply 6

nwmyname

This is not a C1 question, at least not for me as it involves a double derivative.

Reply 7

Tobiq

Original post by nwmyname

This is not a C1 question, at least not for me as it involves a double derivative.

It's from a solomon paper.

Reply 8

nwmyname

Do the d2y/dx2 on the first equation and then subsitute it into the second equation to find a value for k.
Not that hard tho.

Reply 9

KaylaB

Original post by Tobiq

You've found an equation for

\frac{d^{2}y}{dx^{2}}

from part a of the question, and you know the equation of y to be

y = 2x^{\frac{3}{2}} -1

so you can simply plug them in to the equation given to find the value of k

Reply 10

Tobiq

Original post by nwmyname

Do the d2y/dx2 on the first equation and then subsitute it into the second equation to find a value for k.
Not that hard tho.

1. Theres only 1 equation given... what are you talking about?
2. Where does the value of K come from? what does it even represent.

Reply 11

nwmyname

Original post by Tobiq

1. Theres only 1 equation given... what are you talking about?
2. Where does the value of K come from? what does it even represent.

k is something you are going to find.

The first equation right at the top?

Reply 12

Tobiq

Original post by Tobiq

1. Theres only 1 equation given... what are you talking about?
2. Where does the value of K come from? what does it even represent.

In a "show" question you have to arrive at whats given... you cant use it in the solution

Reply 13

nwmyname

Original post by Tobiq

In a "show" question you have to arrive at whats given... you cant use it in the solution

Yes, you show that when you subsitute dy2/dx2, you get a value that is a constant.
A constant being an integer value, e.g. 1 or 2 or 3 or 4.

Reply 14

KingChem

(a) dy/dx= 3x^0.5
d^2y/dx^2=3/2x^-.05
(b) 4x^2(3/2x^-0.5)-3y
6x^3/2-3y=k
3y=6x^3/2-k
y=2x^3/2-1/3k
k=3

Reply 15

Tobiq

Original post by nwmyname

Yes, you show that when you subsitute dy2/dx2, you get a value that is a constant.
A constant being an integer value, e.g. 1 or 2 or 3 or 4.

I've had y'' . What is done next, the only other information given is y=2x^(3/2) - 1;

How do i use y, and y'' to arrive at the equation wielding the K

Reply 16

nwmyname

Original post by Tobiq

I've had y'' . What is done next, the only other information given is y=2x^(3/2) - 1;

How do i use y, and y'' to arrive at the equation wielding the K

Once you differentiate y into dy/dx, you differentiate it again to dy2/dx2.

Then substitute the value that you get.

Original post by Tobiq

Ok, so you have

y'' = \frac{3}{2}x^{-1/2}

and y =

2x^{3/2}-1

The question is, what is the value of

4x^2 y'' -3y

? Because you'll note that the terms involving x are going to cancel out.

Reply 19

Ishan_2000

Original post by Tobiq

I've had y'' . What is done next, the only other information given is y=2x^(3/2) - 1;

How do i use y, and y'' to arrive at the equation wielding the K