Question

Given that `1/y + 1/x = 1/12` and y decreases at a rate of 1 cms^–1, find the rate of change of x when x = 5 cm and y = 1 cm.

Answer 1

Given, `dy/dt` = 1 cm/s

And `1/y + 1/x = 1/12`

On differentiating w.r.t 't' on both sides, we get

`(-1)/y^2 dy/dt - 1/x^2 dx/dt = 0`

Put x = 5, y = 1 and `dy/dt = 1`

∴ `(-1)/1^2 xx 1 - 1/5^2 xx dx/dt = 0`

`\implies - 1 - 1/25 dx/dt = 1`

`\implies (-1)/25 dx/dt = 0`

`\implies dx/dt = - 25`

Hence, the rate of change of 'x' is – 25 cm/sec.