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.