# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2005 | June | Q#7

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Question

a)   Show that can be written as .

Given that , , and that at ,

b)  Find y in terms of x.

Solution

a)

We are given; We have the algebraic formula;          b)

We are required to find y in terms of x, when; We are also given that , and that at .

Clearly it is the case of finding equation from its derivative.

We can find equation of the curve from its derivative through integration;  For the given case; From (a) we know that; Therefore; Rule for integration of is:  Rule for integration of is: Rule for integration of is:       If a point lies on the curve , we can find out value of . We substitute values of and in the equation obtained from integration of the derivative of the curve i.e. .

We are also given that , and that at .

Therefore, substituting given values of y and x.      Hence, above equation obtained from integration can now be written as; 