# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#9

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**Question**

,

**a. **Show that

Where A and B are constants to be found.

**b. **Find

Given that the point (-3,10) lies on the curve with equation y=f(x),

**c. **Find f(x).

**Solution**

**a.
**

We are given;

Therefore;

**b.
**

We are given;

We are required to find .

Second derivative is the derivative of the derivative. If we have derivative of the curve as , then expression for the second derivative of the curve is;

Therefore, for the given case;

As demonstrated in (a);

Therefore;

Rule for differentiation is of is:

Rule for differentiation is of is:

Rule for differentiation is of is:

**c.
**

We are given coordinates of a point on the curve (-3,10).

We are required to find the equation of y in terms of x ie f(x).

We can find equation of the curve from its derivative through integration;

Therefore,

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. .

Therefore, substituting the coordinates of point(-3,10) in above equation;

Therefore, equation of the curve C is;

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