Question

What is the slope of the tangent line to the graph of x2 ? 2xy ? 20 = 0 at the point (2, ?4)?

Answer 1

To determine the slope of the tangent line at the given point (2, -4) for the equation x^2 - 2xy - 20 = 0, implicit differentiation must be used followed by plugging in the x and y values into the derived function to get the slope.

Step-by-step explanation:

To find the slope of the tangent line to the graph of the equation x^2 - 2xy - 20 = 0 at a specific point, we need to use calculus, specifically the derivative of the function. The given point is (2, -4). Here's how to find the slope:

1. First, we need to express y explicitly as a function of x, or x as a function of y, if possible.
2. Then, we take the derivative of that function with respect to x (if y is expressed as a function of x) or with respect to y (if x is expressed as a function of y).
3. Finally, we evaluate the derivative at the given point to find the slope of the tangent line.

Since this equation is not given in the standard y=f(x) or x=g(y) form and cannot be easily solved for one of the variables, implicit differentiation will likely be required. After finding the derivative, we would plug in the x and y values of the given point to find the numerical value of the slope at that point.