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Question 1 of 10

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4. If c is the number defined by Rolle's Theorem, then for f(x) = 2x³ - 6x on the interval [0, √3], c is

A 1 B -1 C 0 D √3 E -√3

Question 2 of 10

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14. A conical reservoir has a diameter of 12 feet and a height of 4 feet with vertex pointing down. Water is flowing into the reservoir at the constant rate of 10 cubic feet per minute. At the instant when the surface of the water is 2 feet above the vertex, the water level is rising at a rate of

A 0.177 ft/min B 0.354 ft/min C 0.531 ft/min D 0.708 ft/min E 0.885 ft/min

Question 3 of 10

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6. A particle moves along the x-axis in such a way that its position at time t, t > 0, is given by x(t) = (ln t)². At what value of t does the velocity attain its maximum?

A 1 B √e C e D e^(3/2) E e²

Question 4 of 10

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17. (1984 AB 5) The volume of a cone is increasing at a rate of 28π in³/sec. At the instant when the radius r is 3 in, its volume is 12π in³ and the radius is increasing at 1/2 in/sec. Find the rate of change of the area of its base.

A 3π sq. in./sec B 6π sq. in./sec C 8 in./sec D 3π/8 in.

Question 5 of 10

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3. The maximum and minimum values of the function f(x) = x³/3 - 5x²/2 + 6x on the closed interval [0, 4] are respectively

A {16/3, 0} B {9/2, 14/3} C {2, 1} D {14/3, 9/2} E {11/2, 5/3}

Question 6 of 10

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8. lim (x→∞) e⁻ˣ ln x =

A 0 B ∞ C 1 D Limit does not exist

Question 7 of 10

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12. If f(x) = ax⁴ + bx² and ab > 0, then

A the curve has no horizontal tangents B the curve is concave up for all x C the curve is concave down for all x D the curve has no inflection point E none of these

Question 8 of 10

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2. How many inflection points does f have?

A 0 B 1 C 2 D 3 E 4

Question 9 of 10

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9. The height of the rectangle with the largest area that can be inscribed under the graph of y = 1 / (1 + 2x²) is

A 2/3 B 1/2 C √2 / 2 D √2 E 1

Question 10 of 10

+1.0 Marks

7. lim (x→0) (e³ˣ - 1) / sin x =

A 0 B 1 C 2 D 3 E does not exist

Calculus - Differentiation & Tangents Review Chapter 2 Part 1

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Calculus - Differentiation & Tangents Review Chapter 2 Part 1

Build Confidence in Mathematics with Expert Guidance