y4 + xy = x3 – x + 84
(a) Find dy/dx at the two points on the graph with x-coordinate 0.
Hint: Set x=0 in the equation and solve for y to find the two points.
Do you mean
y^4 + xy = x^3 - x + 84 ??
if so, then
4y^3 dy/dx + x dy/dx + y = 3x^2 - 1
dy/dx(4y^3 + x) = 3x^2 - 1 - y
dy/dx = (3x^2 - 1 - y)/(4y^3 + x)
now follow the hint
To find dy/dx at the two points on the graph with x-coordinate 0, we first need to find the points themselves. The hint suggests setting x=0 in the equation and solving for y.
Let's substitute x=0 into the equation:
y(0) + 0y = 0^3 - 0 + 84
0 + 0y = 84
0y = 84
y = 0/0 (division by zero is undefined)
We can see that setting x=0 does not yield a well-defined value for y. This means there are no points on the graph with an x-coordinate of 0.
Therefore, we cannot find dy/dx at the two points on the graph with x-coordinate 0 because those points do not exist in this equation.