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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