Question

Find the slope of the tangent line to the curve defined by 9x³ −8xy−3y⁴ =−1899 at the point (−6,1). The slope of the curve at the point (−6,1) is

Answer 1

To find the slope of the tangent line to the curve defined by the equation 9x³ - 8xy - 3y⁴ = -1899 at the point (-6,1), take the derivative of the equation and substitute the coordinates of the point into the derivative.

Step-by-step explanation:

To find the slope of the tangent line to the curve defined by the equation 9x³ - 8xy - 3y⁴ = -1899 at the point (-6,1), we need to take the derivative of the equation and substitute the coordinates of the point into the derivative.

1. Start by taking the derivative of the equation with respect to x. This will give you an expression for the slope at any point on the curve.
2. Next, substitute the x-coordinate of the given point (-6) into the derivative expression to find the slope at that point.
3. Finally, substitute the y-coordinate of the given point (1) into the derivative expression to get the actual value of the slope at the point (-6,1).

The resulting slope will be the slope of the tangent line to the curve at the point (-6,1).