3 3 implicit differentiation homework

For example, the equation y−x2 = 1 y − x 2 = 1 defines the function y = x2 +1 y = x 2 + 1 implicitly. Implicit differentiation allows us to find slopes of tangents to curves that are clearly not functions (they fail the vertical line test).

Find the equation of the line tangent to the graph of y3+x3 −3xy =0 y 3 + x 3 − 3 x y = 0 at the point (3 2, 3 2) ( 3 2, 3 2) ( (Figure) ). This curve is known as the folium (or leaf) of Descartes. Figure 3.

Take the derivatives, so d d x ( x 2) = 2 x and d d x ( y 2) = 2 y d y d x. 2 y d y d x = − 2 x Step 2. Keep the terms with d y d x on the left. Move the remaining terms to the right. d y d x = − x y Step 4. Divide both sides of the equation by 2 y.