The Diagram shows the graph of y = (2 - x)(x + 3).

a) Find the Gradient of the tangent at (-1, 6).

So thats the Q and I have the answers here but Im not sure how they managed to get each step of the working.

Answer;

a) y = (2 - x)(x + 3) = 6 - x - x²

dy/dx = -1 - 2x

When x = -1 dy/dx = -1 - 2 X(-1)

dy/dx = 1

It's mainly the first line of the answer that confuses me. I'm not really sure where it's coming from!

I couldn't upload the diagram of the graph but hopefullt you can tell me without it?

I hope someone can help to make this a little bit clearer, Thanks!

**0**

# Differentiation Question

Started by SockRock16, Oct 23 2008 10:24 AM

5 replies to this topic

### #1

Posted 23 October 2008 - 10:24 AM

### #2

Posted 23 October 2008 - 12:04 PM

Right, well to find the gradient of the tangent you need to differentiate y=(2-x)(x+3), however you can't differentiate that (at least at higher) in its current form so you have to multiply out the brackets

y=(2-x)(x+3)

y=2x+6-x²-3x //which simlifies to

y=6-x-x²

now you can differentiate that so

dy/dx=-1-2x

to find gradient substitute x=-1 into dy/dx

so dy/dx=-1 - 2(-1) = 2-1 = 1

Hope this helps please feel free to ask about anything you still don't understand

y=(2-x)(x+3)

y=2x+6-x²-3x //which simlifies to

y=6-x-x²

now you can differentiate that so

dy/dx=-1-2x

to find gradient substitute x=-1 into dy/dx

so dy/dx=-1 - 2(-1) = 2-1 = 1

Hope this helps please feel free to ask about anything you still don't understand

**=-=-=Marcus=-=-=**### #3

Posted 23 October 2008 - 03:44 PM

That helps a lot now, thanks.

I understand things now but it's most likely that i'll come back with another Question sooner or later! :L

But thanks again!

I understand things now but it's most likely that i'll come back with another Question sooner or later! :L

But thanks again!

### #4

Posted 29 October 2008 - 08:38 PM

weird...lotta ppl r stuck on differentiation which i think isnt TOO bad. also in ur question u have to factorise whicn should leave u with something like x2 + 3x -1 etc then u shood be able to sovle ur problem easily

### #5

Posted 29 October 2008 - 08:40 PM

also why am i a newbie ....thats lame

### #6

Posted 09 November 2008 - 06:54 PM

Thats Great help again! Thanks..

And I understand about the Differentiation thing. My math class has a new teacher and he doesn't explain things to good....

And I understand about the Differentiation thing. My math class has a new teacher and he doesn't explain things to good....

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