a level Differentiation question Watch

DeCosta
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1) The curve with equation y=x^3-4x^2+3x crosses the x-axis at the points A, B and C.
a)find coordinates of points a b and c
b) find the gradient of the curve at each of the points

+

2) A curve has equation y=x^3+x^2-4x+1
a) find the gradient of the curve at the point P(-1,5) <-- ive done this
B) given that the gradient at the point Q on the curve is the same as the gradient at the point P; find, as exact fractions, the coordinates of point Q.

could you show working out cheers in advance
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IceCityRabz
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Do you want answers or help?
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gdunne42
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(Original post by DeCosta)
1) The curve with equation y=x^3-4x^2+3x crosses the x-axis at the points A, B and C.
a)find coordinates of points a b and c
b) find the gradient of the curve at each of the points

+

2) A curve has equation y=x^3+x^2-4x+1
a) find the gradient of the curve at the point P(-1,5) <-- ive done this
B) given that the gradient at the point Q on the curve is the same as the gradient at the point P; find, as exact fractions, the coordinates of point Q.

could you show working out cheers in advance
Question 1a is a round about way of saying solve x^3-4x^2+3x=0 to find points A B and C

In 2a you differentiated the equation to find a gradient function (the derivative)
For 2b you need to solve when that gradient function = the gradient you found in 2a


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DeCosta
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(Original post by IceCityRabz)
Do you want answers or help?
answers please lol
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RDKGames
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(Original post by DeCosta)
answers please lol
If you want answers then just use Wolfram Alpha.

It won't tell you how to do it, and won't help you learn, but hey, answers are the important part, right??
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DeCosta
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(Original post by RDKGames)
If you want answers then just use Wolfram Alpha.

It won't tell you how to do it, and won't help you learn, but hey, answers are the important part, right??
I meant answers with working out, stfu with your sarcastic tone god damn lol
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RDKGames
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(Original post by DeCosta)
I meant answers with working out, stfu with your sarcastic tone god damn lol
Not quite sure how that's supposed to make it any better, but keep up that attitude and you won't even get hints.

We don't really do your questions for you, so post your attempt at the question and we can let you know where you're going wrong or how to proceed. For instance; in Q1 you need to find the roots of the cubic first and then you have your 3 points.
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RossB1702
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(Original post by RDKGames)
If you want answers then just use Wolfram Alpha.

It won't tell you how to do it, and won't help you learn, but hey, answers are the important part, right??
Hey for part A do you do it by setting up a polynomial table and subbing in a value of x that will allow the function = 0 ? That's how I was taught just curious to how you's A level pupils would do it.


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RDKGames
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(Original post by RossB1702)
Hey for part A do you do it by setting up a polynomial table and subbing in a value of x that will allow the function = 0 ? That's how I was taught just curious to how you's A level pupils would do it.


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We would reduce it to something much simpler. So we would factor out the x and then solve the quadratic that is left by either completing the square or factorising it from inspection.
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RossB1702
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(Original post by RDKGames)
We would reduce it to something much simpler. So we would factor out the x and then solve the quadratic that is left by either completing the square or factorising it from inspection.
Oh yeah i didn't spot that you can take out x for each value. how would you do it if you couldn't cancel out the x because there is a positive integer at the end of the function ?
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RDKGames
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(Original post by RossB1702)
Oh yeah i didn't spot that you can take out x for each value. how would you do it if you couldn't cancel out the x because there is a positive integer at the end of the function ?
The problem then becomes more tricky. We would attempt to find at least one root by substituting some factors of the constant. If at least one of those numbers work, we use long division (or otherwise) on the cubic and divide it by (x-a) where x=a makes the cubic equal to 0. This case comes up most of the time at A-Level maths.

What comes up very rarely is when there are no such 'nice' numbers that you try and are factors of the constant, which would make the cubic equal to 0, at which point you can only approximate the roots by various methods or delve into some more complex mathematics beyond normal A-Level maths.
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RossB1702
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(Original post by RDKGames)
The problem then becomes more tricky. We would attempt to find at least one root by substituting some factors of the constant. If at least one of those numbers work, we use long division (or otherwise) on the cubic and divide it by (x-a) where x=a makes the cubic equal to 0. This case comes up most of the time at A-Level maths.

What comes up very rarely is when there are no such 'nice' numbers that you try and are factors of the constant, which would make the cubic equal to 0, at which point you can only approximate the roots by various methods or delve into some more complex mathematics beyond normal A-Level maths.
Interesting. So what are you planning on doing after your degree ?
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RDKGames
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(Original post by RossB1702)
Interesting. So what are you planning on doing after your degree ?
Not entirely sure :lol: but I'd like to go into research
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