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A cannon ball is fired from the top of a cliff and its trajectory is described by the following function:

$$ s(t) = - 12 t^2 + 11 t + 30 $$

Part 1

Compute the average rate of the change of the function $s(t)$ on the time interval $[ 0.375, 1.75 ]$.

Average rate of change is

Sketch the line that represents the graphical interpretation for your result above.

The of the line above provides the average rate of the change of the function $s(t)$ on the time interval $[ 0.375, 1.75 ]$.

Part 2

Compute the instantaneous rate of the change of the function $s(t)$ at time $0.875$.

Instantaneuous rate of change is

For what values of time $t$ will $s'(t)$ be positive?

(a)

0.125

(b)

0.25

(c)

1.25

(d)

1.375

(e)

1.5

(f)

1.75

(g)

1.875

Select all possible options that apply.

Note: this example summarizes the concepts introduced in the previous questions. Read more here.

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QID:

demo/annotated/LectureVelocity/4-KnowledgeTest

Title:

Check what you learned

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Started at:

2026-08-04 20:43:19 (CDT)

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{
  "ts": [
    {
      "key": "a",
      "html": "0.125",
      "feedback": null
    },
    {
      "key": "b",
      "html": "0.25",
      "feedback": null
    }
  ],
  "va": -14.47272727272727,
  "vi": -10,
  "geo": {
    "key": "d",
    "html": "slope",
    "score": 1,
    "feedback": null
  },
  "geo2": {
    "key": "c",
    "html": "secant",
    "score": 1,
    "feedback": null
  },
  "lines": [
    {
      "id": 0,
      "x1": 135,
      "x2": 410,
      "y1": 141,
      "y2": 340,
      "type": "pl-controlled-line",
      "graded": true,
      "stroke": "#ff0000",
      "evented": false,
      "offset_x": 5,
      "offset_y": 5,
      "selectable": false,
      "gradingName": "pl-controlled-line",
      "strokeWidth": 4,
      "drawErrorBox": true,
      "handleRadius": 6,
      "widthErrorBox": 30,
      "heightErrorBox": 30,
      "offset_control_x": 0,
      "offset_control_y": 0,
      "objectDrawErrorBox": null,
      "widthErrorBoxControl": 20,
      "heightErrorBoxControl": 20
    }
  ]
}

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Check what you learned

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