Question

Could someone explain this to me?

Answer 1

This is a simple differentiation problem. Let's start by taking the derivative of both sides (with respect to x):

`5y^4(dy)/(dx)+6y^2x+6x^2y(dy)/(dx)+20x^3 = 0`

Simplify:

`(dy)/(dx) (5y^4+6x^2y) + 6y^2x+20x^3 = 0`

Solve for dy/dx:

`(dy)/(dx) = (-6y^2x-20x^3)/(5y^4+6x^2y)`

Now, plug in the given points:

`(dy)/(dx) = (-6(2)^2(-1)-20(-1)^3)/(5(2)^4+6(-1)^2(2)) = (24+20)/(80+12)`

Further simplification gives:

`(dy)/(dx)|_((2,-1)) =(44)/(92) = (11)/(23)`

So, your answer is 11/23 or B.