Question

2. A curve has equation y = x2 – 2x - 3. A point moves 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.
[3]

Answer 1

The x coordinate of P is
`(4)/(3)`.

Explanation:

Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:

`(dy)/(dt) = 2\cdot x \cdot (dx)/(dt) -2\cdot (dx)/(dt)`

According to the statement of the problem, these variables are known:

`(dx)/(dt) = 6` and
`(dy)/(dt) = 4`

Hence, the x coordinate of P is found by direct substitution:

`4 = 2\cdot x \cdot (6)-2\cdot (6)`

`4 = 12\cdot x -12`

`x = (4)/(3)`

The x coordinate of P is
`(4)/(3)`.