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- 1. Multiple ChoiceThe 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?0.40.60.71.4
- 2. Multiple Choice
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 ChoiceA 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?57.6057.8859.2067.40
- 4. Multiple ChoiceThe 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(0.1)2C
- 5. Multiple ChoiceIf 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 increasingA is always decreasingA is decreasing only when b < hA is decreasing only when b > h
- 6. Multiple ChoiceThe radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?0.04π m2/sec0.4π m2/sec4π m2/sec20π m2/sec
- 7. Multiple ChoiceThe radius of a sphere is decreasing at a rate of 2 cm/sec. At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm2/sec, of the surface area of the sphere? (The surface area of a sphere is A = 4πr2.)-108π-72π-48π-24π
- 8. Multiple ChoiceThe maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle whose velocity is given by v(t) = t3 - 3t2 + 12t + 4 is9121421
- 9. Multiple ChoiceA rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum volume of the solid. (use Calculus)5125150250
- 10. Multiple Choice
Suppose that the sides of a square increase from 3 cm to 3.3 cm. Estimate the change in the area of the square.
1.8 cm2
1.89 cm2
0.9 cm2
19.8 cm2
- 11. Multiple Choice
Using the tangent line approximation for
at x = 9, approximate .3.133
2.867
2.863
2.733
2.712
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