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# Core 2 Question Help ! Watch

1. The gradient of a curve is 6x^2 + 12x^1/2. The curve passes through the points (4,10). Find the equation of the curve. What would i do from start to finish ?

Also another question when differentiation this x - 3/x^2, Would do i do with the 3/x^2?
2. (Original post by Timmy12321)
The gradient of a curve is 6x^2 + 12x^1/2. The curve passes through the points (4,10). Find the equation of the curve. What would i do from start to finish ?
If you know the gradient, you can integrate it to find the equation of the curve. When you integrate, you will get an arbitrary constant , which you should work out using the fact that the curve passes through the point (4,10).

Also another question when differentiation this x - 3/x^2, Would do i do with the 3/x^2?
Writing should help.
3. (Original post by Timmy12321)
Also another question when differentiation this x - 3/x^2, Would do i do with the 3/x^2?
I used to have trouble with these kinds of problems. He's right, writing should help but in order to understand why, you should probably re-visit Indices from Core 1. The main thing you need to know though is that and so The only difference now is when you have a numerator but if you think about then it is easy to work out.
4. (Original post by Timmy12321)
The gradient of a curve is 6x^2 + 12x^1/2. The curve passes through the points (4,10). Find the equation of the curve. What would i do from start to finish ?

Also another question when differentiation this x - 3/x^2, Would do i do with the 3/x^2?
This is an integration question. 6x^2 + 12x^(1/2) becomes 2x^3 + 8x^(3/2) + c = y. Remember, add one to the power, divide by the new power. To find the full equation, sub in your given points, (4,10) 2(4)^3+8(4)(2)+c=10 which becomes 128+64+c=10 c=-182

Therefore the answer is 2x^3 + 8x^(3/2) - 182 = y

The second question is the same as asking for dy/dx of x-3x^(-2). The reverse rule to above applies, nax^(n-1) is the differential. So dy/dx=1+6/(x^3) or 1+6x^(-3). Because -3x x -2 = 6x -2-1=-3

Or at least I hope I'm right.

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6. (Original post by Timmy12321)
I think 80x^3 - 9x^(-2.5), but don't take my word for it.

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7. 20 x^4 + 6x^-3/2

dy/dx = 80x^3 - 9x^-5/2
8. (Original post by Timmy12321)
The gradient of a curve is 6x^2 + 12x^1/2. The curve passes through the points (4,10). Find the equation of the curve. What would i do from start to finish ?

Also another question when differentiation this x - 3/x^2, Would do i do with the 3/x^2?
You're given f'(x). Integrate and you will get f(x), but remember there is a constant that needs finding. f(4)=10 and now find the constant.

I swear this a C1 question.
9. (Original post by Angryification)
You're given f'(x). Integrate and you will get f(x), but remember there is a constant that needs finding. f(4)=10 and now find the constant.

I swear this a C1 question.
It became a C2 question the minute you were given coordinates technically. Before that it is C1 indefinite integration.

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10. (Original post by Cynical_Smile01)
It became a C2 question the minute you were given coordinates technically. Before that it is C1 indefinite integration.

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You can be given coordinates in C1.
11. (Original post by Angryification)
You can be given coordinates in C1.
Depends what exam board.

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12. (Original post by Cynical_Smile01)
Depends what exam board.

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I think OCR don't do it in C1 and keep finite integration to C2

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