How do I solve x^2+4y^3=-828 at pont (-6,-6)

The slope=

To find the slope of the equation x^2 + 4y^3 = -828 at the point (-6, -6), you need to differentiate the equation with respect to either x or y and then evaluate it at the given point.

First, let's differentiate the equation with respect to x:

d/dx (x^2 + 4y^3) = d/dx (-828)

2x + 12y^2(dy/dx) = 0

Now, we need to find dy/dx. To do this, we solve for dy/dx:

dy/dx = -2x / (12y^2)

Now, substitute the given point (-6, -6) into the equation to find the slope at that point:

dy/dx = -2(-6) / (12(-6)^2)
= 12 / (12 * 36)
= 12 / 432
= 1/36

Therefore, the slope of the equation x^2 + 4y^3 = -828 at the point (-6, -6) is 1/36.