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# C3 Turning points Watch

1. bonjour!
please help if you have the know how

y= x.e^2x
find the turning point an determine it's nature.

I know I need to find dy/dx, set it equal to 0, solve for x and then plug that in to find y. I think I know how to determine nature (second diff?)

I'm having trouble with the numbers
2. Ok, what have you done so far? Have you found ?
3. (Original post by Noble.)
Ok, what have you done so far? Have you found ?
I think it's 2x.e^2x but I had trouble solving for x when that =0
4. (Original post by pete.mcfc)
bonjour!
please help if you have the know how

y= x.e^2x
find the turning point an determine it's nature.

I know I need to find dy/dx, set it equal to 0, solve for x and then plug that in to find y. I think I know how to determine nature (second diff?)

I'm having trouble with the numbers
you should have found the derivative: 2x.e^(2x) + e^(2x)

Set this equal to zero, factorise out the e^(2x) term ... and hopefully you will see that x = -0.5

is this what you have so far??
5. (Original post by pete.mcfc)
I think it's 2x.e^2x but I had trouble solving for x when that =0
Unfortunately you have forgotten to use the product rule.. Give it another shot !!
6. (Original post by Mrm.)
Unfortunately you have forgotten to use the product rule.. Give it another shot !!
Thanks, I can do the product rule but I always try and differentiate without it!
Nice one got it now
7. (Original post by pete.mcfc)
I think it's 2x.e^2x but I had trouble solving for x when that =0
Remember the product rule.

8. (Original post by Noble.)
Remember the product rule.

nice one, got that bit.

if dy/dx is 2x.e^2x + e^2x and x= 0.5 and y= 0.184 do i find d2y/dx2 and plug in x to determine nature?
9. (Original post by pete.mcfc)
nice one, got that bit.

if dy/dx is 2x.e^2x + e^2x and x= 0.5 and y= 0.184 do i find d2y/dx2 and plug in x to determine nature?

Are you sure is a solution to ?

Factorise out the and knowing that you should find just one solution (you've got the magnitude correct, just not the sign )

To find you need to just apply the product rule again to , then the rest is just straight differentiation.
10. This might help if you're still stuck.

11. (Original post by Noble.)

Are you sure is a solution to ?

Factorise out the and knowing that you should find just one solution (you've got the magnitude correct, just not the sign )

To find you need to just apply the product rule again to , then the rest is just straight differentiation.
sorry I meant -0.5
i tried to find the second diff without the product rule again!! i am a fool lol, but thaks a million for helping
12. (Original post by pete.mcfc)
sorry I meant -0.5
i tried to find the second diff without the product rule again!! i am a fool lol, but thaks a million for helping
No problem.
13. (Original post by pete.mcfc)
Thanks, I can do the product rule but I always try and differentiate without it!
Nice one got it now
no problem.
14. 1) find dy /dx
2) make dy /dx = 0, and solve for x values
3) find d2y/ dx2, substitute x values in, and determine nature of SP.

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