1. AIM : How do we find tangent lines to a graph? Do Now: Find the slope of the line shown below that goes through points (0,6) and (3,0). HW2.1: p66-67 #9,10,19,22,23

2. What is the slope of y = x 2 at x =1?

3. Secant VS Tangent Secant Line Goes through 2 points Average Rate of Change Ex: (1, 1) and (2, 4) Tangent Line Goes through 1 point Instantaneous ROC Ex: (1, 1)

4. To find the tangent line… …we will approximate the tangent line by using secant lines that get closer and closer to that point! Example: Find the tangent line to y = x 2 at x = 1 X1X1 X2X2 Slope 12 11.5 11.1 11.01

5. Once you have the slope… If you have the slope and a point, how do you find the equation of the line? Your Turn! Find the tangent line to y = x 2 at x = 2

6. More Practice The formula provides a good approximation to the speed of sound, v, in dry air (in m/s) as a function of air temperature, T (in kelvins). a)Compute the average ROC of v with respect to T over the interval [273, 300]. b)Estimate the instantaneous ROC when T = 273 K