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

1 Answer
Apr 26, 2015

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