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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