# 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; 