Core 2 Question Help !

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?

Reply 1

qgujxj39

17

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

C

, 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

\dfrac{3}{x^2} = 3x^{-2}

should help.

Reply 2

iDraw

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

\dfrac{3}{x^2} = 3x^{-2}

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

\dfrac{1}{x} = x^{-1}

and so

\dfrac{1}{x^2} = x^{-2}

The only difference now is when you have a numerator but if you think about

\dfrac{1}{x^2} = 1x^{-2}

then it is easy to work out.

Reply 3

Cynical_Smile01

9

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.

Posted from TSR Mobile

Reply 4

Timmy12321

OP

2

Thanks guys, one last question what about this differentiation 20 x^4 + 6x^-3/2

Reply 5

Cynical_Smile01

9

Original post by Timmy12321

Thanks guys, one last question what about this differentiation 20 x^4 + 6x^-3/2

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

Posted from TSR Mobile

Reply 6

Geek95

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

dy/dx = 80x^3 - 9x^-5/2

(edited 10 years ago)

Reply 7

Angryification

11

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.

Reply 8

Cynical_Smile01

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.