Example 2-5-3 - Maple Help



Chapter 2: Differentiation



Section 2.5: Implicit Differentiation



Example 2.5.3



The curve $y=y\left(x\right)$ defined implicitly by the equation  is called the Folium of Descartes.

 a) Obtain a graph of this curve. In particular, explore the effect of $a$ on the curve.
 b) Obtain $y\prime \left(x\right)$ by implicit differentiation.
 c) Find all points on this curve where its tangent line is horizontal.
 d) Find all points on this curve where its tangent line is vertical.
 e) Working numerically in the case $a=3$, find all points on the curve where its slope is 1. Obtain and graph the corresponding tangent lines.
 f) Solve for $y\left(x\right)$ explicitly in the case $a=3$. Graph the resulting branches.