Question

How to find the slope of the curve at the given point: x^2 + y^2 = 25 ; (3,-4) ?

Answer 1

The slope is the value of the derivative: 3/4

The gradient in `(3,-4)` is `(6,-8)` so we can use the implicit function theorem and locally `y=f(x)` and `f'(x)=-F_x/F_y=-(2x)/(2y)=3/4`