314
Chapter 3 | Derivatives
Figure 3.31 The line y = 3 4
x − 25
4 is tangent to
x 2 + y 2 =25 at the point (3, −4).
Example 3.72 Finding the Equation of the Tangent Line to a Curve
Find the equation of the line tangent to the graph of y 3 + x 3 −3 xy =0 at the point ⎛ ⎝ 3 2 ,
⎞ ⎠ ( Figure 3.32 ). This
3 2
curve is known as the folium (or leaf) of Descartes.
Figure 3.32 Finding the tangent line to the folium of Descartes at ⎛ ⎝ 3 2 , 3 2 ⎞ ⎠ .
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