CIE/GCE/AS/Math/P1/20/Mar/12/Q#4
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;
𝑑𝑦
=4
𝑑𝑡
𝑑𝑥
=6
𝑑𝑡
Rate of change of 𝑦 with respect to 𝑥 is;
𝑑𝑦
𝑑𝑥
We know that;
𝑑𝑦 𝑑𝑦 𝑑𝑡
= ×
𝑑𝑥 𝑑𝑡 𝑑𝑥
Hence;
𝑑𝑦 1
= 4×
𝑑𝑥 6
𝑑𝑦 4
=
𝑑𝑥 6
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;
𝑑𝑦
=4
𝑑𝑡
𝑑𝑥
=6
𝑑𝑡
Rate of change of 𝑦 with respect to 𝑥 is;
𝑑𝑦
𝑑𝑥
We know that;
𝑑𝑦 𝑑𝑦 𝑑𝑡
= ×
𝑑𝑥 𝑑𝑡 𝑑𝑥
Hence;
𝑑𝑦 1
= 4×
𝑑𝑥 6
𝑑𝑦 4
=
𝑑𝑥 6
