# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2020 | Feb-Mar | (P1-9709/12) | Q#4

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**Question**

A curve has equation y = x^{2 }− 2x − 3. A point is moving along the curve in such a way that at P the y-coordinate is increasing at 4 units per second and the x- coordinate is increasing at 6 units per second.

Find the x-coordinate of P.

**Solution**

We are required to find values of x at the points for which;

Rate of change of with respect to is;

We know that;

Hence;

Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is:

Therefore;

We are given that;

Therefore;

Rule for differentiation of is:

Rule for differentiation of is:

Rule for differentiation of is:

We can equate both gradients of the curve;

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