Applications of Derivatives Review 11th - 12th Grade Quiz

Applications of Derivatives Review

Assessment

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Julie Saller

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Mathematics

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11th - 12th Grade

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362 plays

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Hard

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11 questions

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Multiple Choice

1 min

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

Multiple Choice

45 sec

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)

Multiple Choice

5 mins

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

Multiple Choice

2 mins

1 pt

The radius of a circle is decreasing at a constant rate of 0.1 cm/sec. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

-(0.2)πC

-(0.1)C

(0.1)²C

Multiple Choice

3 mins

1 pt

If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?

A is always increasing

A is always decreasing

A is decreasing only when b < h

A is decreasing only when b > h