Modeling Rates of Change: Quiz

Problem 4

Consider the following table of values of an unknown distance function D(t), its first and second derived values.

t D(t) first derived second derived
–4 9.2 –2.5 0.4
–3.5 7.95 –2.3 0.4
–3 6.8 –2.1 0.4
–2.5 5.75 –1.9 0.4
–2 4.8 –1.7 0.4
–1.5 3.95 –1.5 0.4
–1 3.2 –1.3 0.4
–0.5 2.55 –1.1 0.4
0 2 –0.9 0.4
0.5 1.55 –0.7 0.4
1 1.2 –0.5 0.4
1.5 0.95 –0.3 0.4
2 0.8 –0.1 0.4
2.5 0.75 0.1 0.4
3 0.8 0.3 0.4
3.5 0.95 0.5
4 1.2

Which of the following conclusions are supported by the table?

  1. D(t) is quadratic.
  2. The acceleration function is constant.
  3. Because t is increasing, D(t) describes a falling object.
  4. The velocity function is constant.
  5. The instantaneous velocity at any point is zero.
  6. D(t) will increase without bound as t gets larger.

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