AP Calc AB questions

tb0mb93
Tue, 28 Dec 2010 20:38:36 +0000

What is the approximate slope of the tangent to the curve x^3+y^3=xy at x = 1?


Implicit differentiation

Start by taking the derivative of the left side, and then chain rule for the right
3x^2 + (3y^2)dy/dx = y + x(dy/dx)

Get the dy/dx ‘s to the same side and solve for it. That is the derivative/slope so thats where you’ll plug in the value x=1. You will also need a y-value so plug x=1 into the original function to get the y-value, plug that into f’(x)