1. For the function f(x) = x, find the slope of secants over each of the following intervals: a. x = 2 to x = 3 b. x = 2 to x = 2.5 c. x = 2 to x = 2.1 d. x = 2 to x = 2.01 e. x = 2 to x = 2.001 2. Using that data that you collected in question 1, what do you think the slope of the tangent to f(x) = x3 at the point (2, 8) would be? Explain you answer. 3. Using an online graphing/software (Desmos/Geogebra/Excel), graph the equation f(x) = x and show the tangent at the point (2, 8). Insert this graph (both the function and the tangent line) in your assignment. (ie. show this graph) Assistance : Creating a tangent line with Desmos. 4. A science project studying catapults sent a projectile into the air with an initial velocity of 45 m/s. The formula for height (s) in meters with respect to time in seconds is s(t) = -4.912 + 45t. i/ Calculate the average rate of change (average velocity) of the height over the intervals listed. a. from t=1 to t=3 b. from t=2 to t=3 c. from t=2.5 to t=3 d. from t=2.9 to t=3 e. What do you think might be happening close to t=3? Why? ii/ Calculate the instantaneous rate of change (velocity) at t = 4 seconds