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To answer this question, we must use our knowledge of integration and differentiation. 
First, we look at the information given to us. We have been told that the gradient of the curve is given by dy/...

Extracted from Cambridge International Examinations / MATHEMATICS 9709/11 Paper 1 Pure Mathematics 1

(7 points out of 10 for this question)

A line has equation y = 2x + c an...

To differentiate this kind of expression you would need to use implicit differentiation. 

Although it may sound new, you already have all the skills you need to be able to do it. We will ...

First of all note the dx means that we are integrating with respect to x.

So lets integrate each term seperately..

3x^2 ---> (raise the power by one then divide by the ne...

Fristly, we should integrate the whole equation,

y=∫ 6-8x+x^4 dx

y=6x-4x^2+x^5/5+C

Then, subsitituting values to find the C,

4=61-41^2+1...