# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | January | Q#7

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**Question**

A curve with equation y = f (x) passes through the point (2,10).

Given that

f ′(x) = 3x^{2 }− 3x + 5

find the value of f (1).

**Solution**

We are required to find f(1) but we are not given f(x) but f ′(x).

f ′(x) = 3x^{2
}− 3x + 5

Therefore, we need to find f(x).

We are also given that the curve passes through the point P(2,10).

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 the curve passes through the point (2,10).

Therefore, substituting given values of y and x.

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

Now we can find by substituting x=1 in above obtained equation.

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