(Solved): The accompanying graph shows the total distance s traveled by a bicyclist after \( t \) hours. (a ...

The accompanying graph shows the total distance s traveled by a bicyclist after \( t \) hours. (a) Which of the following is the bicyclist's average speed, in \( \mathrm{mph} \), over the time interval \( [0,1] \) ? A. \( 62 \mathrm{mph} \) B. \( -62 \mathrm{mph} \) C. \( -12 \mathrm{mph} \) D. \( 12 \mathrm{mph} \) (b) Which of the following is the bicyclist's instantaneous speed, in \( \mathrm{mph} \), at \( \mathrm{t}=3 \mathrm{hrs} \) ? A. \( 0 \mathrm{mph} \) B. \( -25 \mathrm{mph} \) C. \( -25 \mathrm{mph} \) D. \( 25 \mathrm{mph} \) (c) Which of the following choices gives the maximum speed, in \( \mathrm{mph} \), and the time at which it occurs? A. The maximum speed of the bicyclist is \( 25 \mathrm{mph} \) and it occurs when \( t=1 \mathrm{hr} \). B. The maximum speed of the bicyclist is \( 25 \mathrm{mph} \) and it occurs when \( t=3.5 \mathrm{hrs} \). C. The maximum speed of the bicyclist is \( 50 \mathrm{mph} \) and it occurs when \( t=3.5 \mathrm{hrs} \). D. The maximum speed of the bicyclist is \( 50 \mathrm{mph} \) and it occurs when \( t=1 \mathrm{hr} \).