Question

The equation of a curve C is given by

(5+x y)²=x+y-4 .
(a) Using implicit differentiation, find the slope y' of the curve at the point P(5,-1).

Answer 1

To find the slope of the curve at the point P(5,-1), we can use implicit differentiation and solve for dy/dx. Substituting in the point, we can find the slope y' of the curve at that point.

Step-by-step explanation:

To find the slope of the curve at the point P(5,-1), we can use implicit differentiation. Start by differentiating both sides of the equation with respect to x. Then, solve for dy/dx which represents the slope of the curve.

To find dy/dx, we can use the chain rule. Differentiating (5+x)y² gives us 2(5+x)y*dy/dx. Differentiating (x+y-4) gives us 1+dy/dx. Setting these two derivatives equal to each other, we can solve for dy/dx.

Substituting in the point P(5,-1), we can find the slope y' of the curve at that point.