8. pro F9 + backspace Kum lock 7 home 8 9 pg up 7. Consider the function f(x) if x 0 = Does f'(0) exist? 0 if x = 0. Justify your answer by applying the limit definition of the derivative. The graph of a function f(t) shown in the figure gives the position of a model car moving along a straight line as a function of time. Use the slopes of f(t) at the indicated values of t to sketch the graph of f'(t), the velocity curve for the car. s (ft) 35 Slope = 4- Slope = 0 30 Slope = -3 25+ 10 8. 20 Slope = 10 6- 15+ Slope = -3.5 Slope = -6 4 10 Slope = 0 T Slope 5 Slope = 4! I = -3 Slope = 0 2- T J H + +++ 11 13.. 0 15. ..17.. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 t (sec) -2- -4 Estimate the velocity of the car when: -6- a. t=5 b. t = 12