Question

Find the slope of the tangent line to the curve 5x+8y + 2xy=10 at the point (4,2). The slope of the tangent line to the curve at the given point is

Answer 1

To find the slope of the tangent line to the curve at the point (4,2), one must first implicitly differentiate the equation and then solve for dy/dx. Substituting the point (4,2) gives the desired slope.

Step-by-step explanation:

The student has asked to find the slope of the tangent line to the curve 5x+8y+2xy=10 at the point (4,2). To find the slope, we first need to implicitly differentiate the equation with respect to x.

1. Differentiate both sides of the equation with respect to x, remembering to apply the product rule to the term 2xy.
2. After differentiating, solve for dy/dx, which represents the slope of the curve at any point (x,y).
3. Substitute the coordinates of the given point (4,2) into the differentiated equation to find the slope of the tangent at that point.

The result is the slope of the tangent line to the curve at the point (4,2).