A. Equations of Normal and Tangent Lines

1. The tangent and normal line to y=?x²+9 at (4, 5). 2. The tangent and normal line to y=?16+x² at the origin . 3. The tangent and normal line to ?9x³?y³=1 at (1, 2).

B. Related Rates

1.We want to build a greenhouse that has a half-cylinder roof of radius r and height r mounted horizontally on top of four rectangular walls of height h as shown in the figure. We have 200? m² of plastic sheet to be used in the construction of this structure. Find the value of r for the

greenhouse with the largest possible volume we can build.