x Turn on thread page Beta
 You are Here: Home >< Maths

# C3 Differentiation Urgent Help needed!!! watch

1. anyone?
2. (Original post by jordanwu)
Ok thanks guys I got to the answer.
So the next part is: find the value of x at which the gradient of the curve is 1/12, giving your answer to 3sf.
So 1/12=(1/2 + cos (x/2)/(2 + cos (x/2))^2 , but I keep getting stuck on rearranging. Any tips?

Expand, solve for cos(x/2) and then x.
3. (Original post by keromedic)

Expand, solve for cos(x/2) and then x.
Hmm I got cos^2 (x/2) - 6cos (x/2) + 4 = 0
No idea how xD...
4. (Original post by keromedic)

Expand, solve for cos(x/2) and then x.
Hang on I've now got cos^2(x/2) - 8cos(x/2) - 2 = 0, how would you factorise that?
5. (Original post by jordanwu)
Hang on I've now got cos^2(x/2) - 8cos(x/2) - 2 = 0, how would you factorise that?
I'm not really following your working but assuming you've done everything right so far..

How would you factorize ?
6. (Original post by keromedic)
I'm not really following your working but assuming you've done everything right so far..

How would you factorize ?
By completing the square/quadratic formula because it can't be factorised?
So by cts I got x=4plusorminus sqrt(18), so cos(x/2)=4plusorminus sqrt(18)??
7. (Original post by keromedic)
I'm not really following your working but assuming you've done everything right so far..

How would you factorize ?
Am I in the right direction or completely wrong with my answer?
8. (Original post by jordanwu)
By completing the square/quadratic formula because it can't be factorised?
So by cts I got x=4plusorminus sqrt(18), so cos(x/2)=4plusorminus sqrt(18)??
Yes, that looks right

Posted from TSR Mobile
9. How would I then determine the range of values of x for which y is increasing, leaving my answer in terms of pi?
dy/dx>0 when y is increasing?
10. Anyone?
11. (Original post by jordanwu)
How would I then determine the range of values of x for which y is increasing, leaving my answer in terms of pi?
dy/dx>0 when y is increasing?
Yes.
12. (Original post by SeanFM)
Yes.
So do I set the expression for dy/dx > 0? Where would I get the pi from?
13. (Original post by jordanwu)
So do I set the expression for dy/dx > 0? Where would I get the pi from?
The pi bit will become clear when you set dy/dx > 0, then think about the denominator, then the numerator.
14. (Original post by SeanFM)
The pi bit will become clear when you set dy/dx > 0, then think about the denominator, then the numerator.
I'm sorry but I'm not sure what you mean, am I meant to rearrange or solve for x or?
15. (Original post by jordanwu)
I'm sorry but I'm not sure what you mean, am I meant to rearrange or solve for x or?
Remember that dy/dx > 0 means that dy/dx is always positive.

You do require an inequality from the expression for dy/dx but it's not from the whole fraction. Then look back at my previous hint.
16. (Original post by SeanFM)
Remember that dy/dx > 0 means that dy/dx is always positive.

You do require an inequality from the expression for dy/dx but it's not from the whole fraction. Then look back at my previous hint.
Well am I meant to find x to find the critical value?
17. (Original post by jordanwu)
Well am I meant to find x to find the critical value?
You don't need to do that, it's a bit more simple than that.

When is dy/dx a positive number? In terms of the expression of dy/dx given in this question, I'm not looking for 'when y is increasing wrt x'.)
18. (Original post by SeanFM)
You don't need to do that, it's a bit more simple than that.

When is dy/dx a positive number? In terms of the expression of dy/dx given in this question, I'm not looking for 'when y is increasing wrt x'.)
dy/dx is positive when the gradient is positive which is the same thing.. sry I really don't know
19. Not to worry. If I said that , where a and b are variables that can be any positive or negative number when is dy/dx positive? (For what values of a and/or b?)

(Original post by jordanwu)
dy/dx is positive when the gradient is positive which is the same thing.. sry I really don't know
20. (Original post by SeanFM)
Not to worry. If I said that , where a and b are variables that can be any positive or negative number when is dy/dx positive? (For what values of a and/or b?)
The numerator would have to be positive for dy/dx to be positive, the denominator can be either positive or negative as squaring either a +ve or -ve number is still +ve?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 22, 2015
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams