1. 1.6 – Tangent Lines and Slopes Slope of Secant Line Slope of Tangent Line Equation of Tangent Line Equation of Normal Line Slope of Tangent = 0 3.1

2. Given the curve: x f(x) x+h f(x+h)

3. Given the equation a) Find the slope of a secant line through the given point

4. Given the equation b) Find the SLOPE of a tangent line through the given point From part a, At (4, 0), 2x – 4 = 2(4) – 4 = 4 c) Find the EQUATION of a tangent line through the given point From part b, we have the slope (4)….and we have the pt (4, 0) y – 0 = 4(x – 4) c) Find the value of x for which the slope of the tangent line is 0 2x – 4 = 0 x = 2

5. Given the equation a) Find the slope of a secant line through the given point

6. b) Find the SLOPE of a tangent line through the given point From part a, At (1, -1), c) Find the EQUATION of a tangent line through the given point From part b, we have the slope (1)….and we have the pt (1, -1) y + 1 = 1(x - 1) c) Find the value of x for which the slope of the tangent line is 0 Given the equation

7. Using the limit definition, find the first derivative of

10. When will the slope of the tangent to be equal to zero? The slope of the tangent line is the first derivative We just computed the first derivative. The numerator of the fraction is never zero Therefore, the slope of the tangent is never zero.

11. Find the equation of the line normal to