Question

A curve has equation `y=k/x`. Given that the gradient of the curve is `-3` when `x=2`. Find the value of constant `k.`?

A curve has equation `y=k/x`. Given that the gradient of the curve is `-3` when `x=2`. Find the value of constant `k.`

Answer 1

`k=12`

Explanation:

`•color(white)(x)m_(color(red)"tangent")=dy/dx" at x = 2"`

`y=k/x=kx^-1`

`rArrdy/dx=-kx^-2=-k/x^2`

`-k/x^2=-3" when "x=2`

`rArr-k=-3xx4=-12rArrk=12`