Mathematics

11th -

12thgrade

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Applications of Derivatives Review

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  • 1. Multiple Choice
    1 minute
    1 pt
    The function f is twice differentiable with f(2) = 1, f'(2)=4, and f''(2)=3.  What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2?
    0.4
    0.6
    0.7
    1.4
  • 2. Multiple Choice
    45 seconds
    1 pt

    Suppose that for a twice differentiable function f (x), f '(x) > 0 and f ''(x) > 0 on the interval (1,3). If we use a linear approximation at x = 2 to estimate f (1.9), will that estimate be an underestimate or overestimate, and why?

    Underestimate since f '' > 0 on (1, 3)

    Overestimate since f '' > 0 on (1,3)

    Underestimate since f ' > 0 on (1, 3)

    Overestimate since f ' > 0 on (1, 3)

  • 3. Multiple Choice
    5 minutes
    1 pt
    A railroad track and a road cross at right angles.  An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second.  At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection?
    57.60
    57.88
    59.20
    67.40
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