Question

Question #f73f9

Answer 1

`m=-1/10`

Explanation:

`color(orange)"Reminder "m_("tangent")=dy/dx`

differentiate `color(blue)"implicitly with respect to x"`

Both terms on the left side require to be differentiated using
the `color(blue)"product rule"`

`(x.3y^2dy/dx+y^3 .1)+(x.dy/dx+y.1)=0`

`rArr3xy^2dy/dx+y^3+xdy/dx+y=0`

`rArrdy/dx(3xy^2+x)=-y^3-y`

`rArrdy/dx=-(y^3+y)/(3xy^2+x)`

Substitute the coordinates of (5 ,1) into `dy/dx`

`rArrdy/dx=-2/(15+5)=-1/10`