1. Given the function g(x) = 2-x-x, calculate a) the Net Change and b) the Average...

  

Transcribed Image Text:

1. Given the function g(x) = 2-x-x, calculate a) the Net Change and b) the Average Change over the interval: [-3,0]. 2. A stone is tossed vertically upwards from the ground and its position is described by s(t) = 36t - 16t a) Compute the stones average velocity over the time interval [0.25, 1.5]. b) To the graph of this function add the points (0.25, s(0.25)) and (1.5, S(1.5)) and include the secant line between these two points. c) Compute the stone's average velocity over the time intervals [1, 1.01], [1, 1.001], [1, 1.0001] and [0.99,1], [0.999, 1], [0.9999, 1]. Use these calculations to estimate the instantaneous velocity at t = 1. d) The instantaneous velocity from step c is the slope of the line tangent at the point (1, 20). Write the equation of the tangent line at this point on the curve when t = 1. 3. Add the tangent line to the graph. 20 16 12 05 N 25 1. Given the function g(x) = 2-x-x, calculate a) the Net Change and b) the Average Change over the interval: [-3,0]. 2. A stone is tossed vertically upwards from the ground and its position is described by s(t) = 36t - 16t a) Compute the stones average velocity over the time interval [0.25, 1.5]. b) To the graph of this function add the points (0.25, s(0.25)) and (1.5, S(1.5)) and include the secant line between these two points. c) Compute the stone's average velocity over the time intervals [1, 1.01], [1, 1.001], [1, 1.0001] and [0.99,1], [0.999, 1], [0.9999, 1]. Use these calculations to estimate the instantaneous velocity at t = 1. d) The instantaneous velocity from step c is the slope of the line tangent at the point (1, 20). Write the equation of the tangent line at this point on the curve when t = 1. 3. Add the tangent line to the graph. 20 16 12 05 N 25