1. Aim: Finding the slope of the tangent line using implicit differentiation Do Now: Find the derivative 1)y³ + y² - 5y – x² = -4 2) y = cos (xy) 3) √xy = x – 2y HW #23 – pg 139 #17,19,21,24,25

2. Finding the slope of the tangent line implicitly 1)Find the derivative implicitly 2)Plug in the values for x and y to find the slope. Example: Find the slope of the tangent line for x² + 4y² = 4 at (√2, -1/√2)

3. Other Examples: 1)x² - y³ = 0 at (1,1) 2)(x + y)³ = x³ + y³ at (-1,1)

4. To find the equation of the tangent line: Find the (derivative)slope – use the slope and the coordinate pair to find the equation – either point-slope or slope-intercept form. Find the equation of the tangent line: 1) x² + y² = 20 at (2,4)

5. Try these: 1)x² - y² = 16 at (5,3) 2)3(x² + y²)² = 100xy at (3,1)