You are Here: Home >< Maths

# Finding stationary point watch

1. In 8i, I keep getting x=8 instead of x=4 like in the mark scheme. Can someone please show the working? (probably my algebra is wrong)
2. When I do part ii, I also keep getting x=8 instead of x= 8 or 0.
3. What did you get when you differentiated?

4. I got -x(8x-x^2)^-0.5.
5. I don't agree.

How are you doing it, can you show me your working? It looks as though you are not differentiating correctly.

Meanwhile I'll do the working to show you.
7. I see that it’s x(8x-x^2)^-0.5. But when I make it equal to 0 to find the stationary point, I don’t know how to find x.
8. I think you've only done half the differentiation (and not done it right)

To me this is 'function of a function' and I'd do it like this (think sometimes called 'chain rule')

Not sure what notation you use but I would do this

y = (8x - x²) ^1/2

So y = f ^1/2 where f = (8x - x²)

dy/df = 1/2 f ^(-1/2) and df/dx = 8- 2x That bit in bold just because I think it's the key to the solution here

dy/dx = dy/df . df/dx = 0.5 (8x - x²) ^(-1/2) . (8 - 2x)

= 1/2 (8 - 2x) / (8x - x²)^1/2

To make this = zero we need the top bit to equal zero therefore 8 - 2x = 0 and solve for x
9. Thank you, but how did you make it into division in the last line of your working?
10. Differentiating the (.... ) ^1/2 bit makes it 1/2 ( ....) ^-1/2

So that -1/2 power means I can put it on the bottom and make the power + instead
11. Thank you so much phys981! You have probably raised me a grade already.

### Related university courses

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: March 1, 2018
Today on TSR

### He lied about his age

Thought he was 19... really he's 14

### University open days

Wed, 25 Jul '18
2. University of Buckingham
Wed, 25 Jul '18
3. Bournemouth University
Wed, 1 Aug '18
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