2.2 The Derivative: Instantaneous Rate of Change

Checkpoint 1

  1. Figure C1 shows a portion of the graph of `s=ct^2`. Note that the function values on the vertical scale are multiples of the constant `c`. Use this figure to calculate the instantaneous speed at the instant `t = 5 text(.)` (Your answer should contain the constant `c`.)

    Figure C1   A zoom-in view of the graph of s = ct2.

  2. Recall that `c` is approximately `4.90 text(.)` Find the numerical value of the instantaneous speed (in meters per second) of an object that has been falling for `5` seconds.

  3. Does this agree with your estimate in Activity 1?