l) A potato is placed in an oven, and the potato's temperature F (in degrees Fahrenheit) at various points in time is taken and recorded in the following table. Time t is measured in minutes. F (t) 70 180.5 251 296 324.5 342.8 354.5 a) Use a central difference to estimate F '(45). Use this estimate as needed in subsequent questions. b) Find the local linearization y = L (t) to the function y = F (t) at the point where a = 45 . c) Use the local linearization to determine an estimate for F (47) . d) Do you think your estimate in (c) is too large or too small? Why? 2) Find the rst and second derivatives of the function f (t) = % i 8'. Use DEMOS to verify your solutions graphically. x_3_4 3) Find the equation ofthe line tangent to f(x) at x = 2 if f(x) = 2 3 , 1: Clearly show your work using derivative rules (not the limit denition). Confirm that your answer looks reasonable graphically using Desmos