Consider the data below for a car tire with a leak: Minutes after the leak began Pressure of air in the tire in kilopascals (kPa) ARL = 0 400 5 335 (23 170-400 30 10 295 15 255 20 225 25 195 a) Calculate the average rate of change over the 30 minute interval. Explain the meaning of this rate using proper units. = -7.67 b) Estimate the instantaneous rate of change at 5 minutes using a surrounding interval. 30 170 3) For the function f(x)=x-3x+2 a) Calculate the average rate of change for the following intervals i)-1 x 2 ii) 4 x 8 0- 6 42-6 4 b) Use the graph of the function to estimate the instantaneous rate of change at x = 2 by drawing a tangent line and calculating it's slope. 2 -2 mtr c) Verify your answers from part b) by calculating the LIMIT of the secant slopes as you approach x = 2. Ay Slope of secant = Ax Interval 2 x 2.5 2 x 2.1 2x 2.01 2x 2.001 Estimate of instantaneous rate of change at x = 2 ... Ay 25 4) Use the data below for the temperature in degrees Celsius for a wood fire oven. Time in Minutes 0 8 13 15 205 Temp (C) 280 290 5 120 Ax 10 250 19 290 21 285 25 285 a) Find the average rate of change of the temperature between 0 and 25 minutes. Show proper units and notation. b) Estimate the instantaneous rate of change of the temperature at 10 minutes. Use 2 methods. 5) Find the equation of the derivative for each of the following functions. Also, find the instantaneous rate of change for the function when x = -2 and x = 3. a) f(x) = 4x - 1 c) f(x) = -2x + 3x b) f(x) = 3x - 5x + 2 6) Determine the equation of the tangent line at x = -2 for the function in part f(x) = 3x - 5x+2