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C3 Help.

Hey,

How would I show that the differentiation of:-

1 - (2)/(3x^2+2) with a domain of (0,infinite) is always positive? When I differentiate it I get - (12x)/(3X^2+2)^2. Or have I differentiated it wrong? :colondollar: Any help please? Thank you. :smile:
Reply 1
I can't see what you've written. Too many brackets. Also the use of - doesn't help especially in the first instance. I can hazard a guess though.
Reply 2
Original post by StephenP91
I can't see what you've written. Too many brackets. Also the use of - doesn't help especially in the first instance. I can hazard a guess though.


Sorry, the - is minus sign. I can't use latex :frown:.
Reply 3
Original post by FutureMedic
Sorry, the - is minus sign. I can't use latex :frown:.


That's not my problem. The first line. 1-(2). Are you saying 1-2 or is it question 1? and then it says -(2) ?

If it is minus 2, you end up with:

12x(3x2+2)2\dfrac{12x}{(3x^{2} + 2)^{2}}

Then you can just simply say 12x12x is always a positive value for x belonging to the positive real numbers and since the domain is only the positive reals then this is fine. (3x2+2)2(3x^{2} + 2)^{2} is postive regardless of whether or not x is negative or positive. Then just conclude saying that a positive value divided by a positive value is always positive.
(edited 13 years ago)
Reply 4
Differentiate again to find d2y/dx2
Reply 5
Original post by StephenP91
That's not my problem. The first line. 1-(2). Are you saying 1-2 or is it question 1? and then it says -(2) ?

If it is minus 2, you end up with:

12x(3x2+2)2\dfrac{12x}{(3x^{2} + 2)^{2}}

Then you can just simply say 12x12x is always a postively value for x belonging to the positive real numbers. (3x2+2)2(3x^{2} + 2)^{2} is postive regardless of whether or not x is negative or positive. Then just conclude saying that a positive value divided by a positive value is always positive.


Hi,

It's 1 minus the fraction numerator (2), denominator (3x^2+2). :smile:
(edited 13 years ago)
Reply 6
Original post by FutureMedic
Hi,

It's 1 minus the fraction numerator (2), denominator (3x^2+2)^2. :smile:


Alrighty then. Just read what I said in the previous post.
Reply 7
Original post by StephenP91
Alrighty then. Just read what I said in the previous post.


Thank you. :smile:
Reply 8
Original post by StephenP91
Alrighty then. Just read what I said in the previous post.


Isn't there a minus when it's differentiated though coming from the ^-1? :s-smilie:
Reply 9
Original post by FutureMedic
Isn't there a minus when it's differentiated though coming from the ^-1? :s-smilie:


23x2+2\dfrac{-2}{3x^{2}+2}

The minus 1 you bring up is made plus by your -2.

(3x2+2)1(3x^{2}+2)^{-1}

Differentiate that.

6x(3x2+2)2-6x(3x^{2}+2)^{-2}

Then when you multiply that by the -2, you get what I previously said.
(edited 13 years ago)

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