# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | January | Q#8

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**Question**

The curve with equation y=f (x) passes through the point (1,6). Given that

, ,

find f(x) and simplify your answer.

**Solution**

We are required to find f(x), when;

We are also given that , and the curve passes through the point (1,6).

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;

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 the curve passes through the point (1,6).

Therefore, substituting given values of y and x.

Hence, above equation obtained from integration can now be written as;

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