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What is the correct answer?

4

If f(x) = x^3 + 2x^2 - 5x + 1, what is f''(x)?

A. 3x^2 + 4x - 5

B. 6x + 4

C. 6x^2 + 4

D. 3x^2 + 4

Correct Answer :

A. 3x^2 + 4x - 5


Related Questions

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4

Which of the following limits does not exist?

A. lim (x -> 0) (1/x)

B. lim (x -> 2) (x^2 - 4)/(x - 2)

C. lim (x -> 1) (x^2 - 1)/(x - 1)

D. lim (x -> 3) (1/x^2)

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4

If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?

A. 25

B. 33

C. 41

D. 49

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4

What is the directional derivative of the function f(x, y) = x^2 + y^2 at the point (1, 2) in the direction of the vector v = <3, 4>?

A. 1

B. 2

C. 3

D. 4

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4

Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?

A. Separable

B. Linear

C. Exact

D. Homogeneous

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4

What is the general solution to the differential equation dy/dx = 3x^2?

A. y = x^3 + C

B. y = 3x + C

C. y = x^3/3 + C

D. y = 3x^3 + C

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4

If the rate of change of a quantity is given by f'(t) and ?(0 to 4) f'(t) dt = 10, what can you conclude about the quantity at t = 4?

A. The quantity is 10 at t = 4.

B. The quantity is 0 at t = 4.

C. The quantity is increasing at t = 4.

D. Nothing about the quantity at t = 4 can be determined.

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4

What does the definite integral ?(a to b) f(x) dx represent geometrically?

A. The average value of f(x) on [a, b]

B. The area between the curve y = f(x) and the x-axis on [a, b]

C. The derivative of f(x) at x = a

D. The slope of the tangent line to the curve y = f(x) at x = b

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4

What is a vector?

A. A point in space

B. A scalar quantity

C. A quantity with magnitude and direction

D. A constant value

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4

If f(x) = sin(x), what is f'(x)?

A. cos(x)

B. -cos(x)

C. sin(x)

D. -sin(x)

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4

What is the distance between the points A(2, -1, 3) and B(4, 3, -2)?

A. v42

B. v30

C. v29

D. v35

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4

Which method is commonly used to solve separable differential equations?

A. Laplace transforms

B. Substitution

C. Separation of variables

D. Variation of parameters

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4

Which of the following functions is continuous at x = 2?

A. f(x) = 1/x

B. g(x) = x^2 + 3x + 2

C. h(x) = |x - 2|

D. None of the above

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4

What is the unit vector in the direction of vector v = <4, -3>?

A. <1, 1>

B. <2, -1.5>

C. <4/5, -3/5>

D. <0, 0>

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4

Which test is used to determine the convergence or divergence of an infinite series involving alternating terms?

A. Integral Test

B. Comparison Test

C. Alternating Series Test

D. Divergence Test

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4

Which of the following is an exact differential equation?

A. dy/dx = 2xy

B. dy/dx = x^2 + y^2

C. dy/dx = e^x

D. dy/dx = y^2 - x^2

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4

If a car's speed is decreasing over time, what can you conclude about its acceleration?

A. The acceleration is positive.

B. The acceleration is negative.

C. The acceleration is zero.

D. Nothing about the acceleration can be determined.

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4

What is the integral of 3x^2 with respect to x?

A. x^3 + C

B. x^2 + C

C. x^3/3 + C

D. 3x + C

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4

What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?

A. y = x^2 + 1

B. y = x^2

C. y = 2x + 1

D. y = 2x

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4

What is the average value of the function f(x) = 2x^2 on the interval [1, 3]?

A. 4/3

B. 8/3

C. 16/3

D. 32/3

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4

In three-dimensional space, what are the coordinates of the origin?

A. (0, 0, 0)

B. (1, 1, 1)

C. (0, 0)

D. (1, 1)

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4

What is the derivative of ln(x) with respect to x?

A. 1/x

B. 1

C. x

D. 0

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4

What is the limit of f(x) as x approaches 3 for the function f(x) = 2x + 1?

A. 5

B. 6

C. 7

D. 8

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4

If a plane is defined by the equation 2x - 3y + z = 7, what is the normal vector to the plane?

A. <2, -3, 1>

B. <3, 2, -1>

C. <1, 3, -2>

D. <-2, 3, -1>

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4

What is the equation of a sphere with center (1, -2, 3) and radius 4?

A. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 4

B. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 16

C. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 4

D. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 16

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4

If the velocity of an object is given by v(t) = 3t^2, what does ?(1 to 2) v(t) dt represent?

A. The total distance traveled by the object from t = 1 to t = 2

B. The acceleration of the object at t = 1

C. The change in velocity of the object from t = 1 to t = 2

D. The displacement of the object at t = 2

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4

What is the limit of (sin x) / x as x approaches 0?

A. 1

B. 0

C. -1

D. Undefined

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4

What is the antiderivative of e^(2x) with respect to x?

A. e^(2x) + C

B. (1/2)e^(2x) + C

C. (1/2)e^(2x^2) + C

D. (1/4)e^(2x) + C

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4

The integral ?(0 to 1) x^3 dx is equal to:

A. 0

B. 1/4

C. 1/3

D. 1/2

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4

What is the derivative of f(x) = 4x^3 - 2x^2 + 5x - 1 with respect to x?

A. 12x^2 - 4x + 5

B. 12x^2 - 4x - 5

C. 12x^2 - 2x + 5

D. 12x^2 - 2x - 5

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4

If a particle's position at time t is given by r(t) = <3t, t^2, 2t - 1>, what is its velocity vector v(t)?

A. v(t) = <3, 2t, 2>

B. v(t) = <3t, t^2, 2t - 1>

C. v(t) = <3t^2, 2t, 2>

D. v(t) = <2, 2t, 2t - 1>