AP Calculus AB Multiple Choice

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Home>Mathematics homework help>Calculus homework help>AP Calculus AB Multiple Choice

1. 

Which one of the following does not find the value of f '(5) for f(x) = 3x2 - 2x - 4? (4 points)

 

All of these find the value for f '(5).

f prime of 5 equals the limit as h approaches 0 of the quotient of the quantity 3 times the square of the quantity 5 plus h minus 2 times the quantity 5 plus h minus 4 minus 3 times 5 squared plus 2 times 5 plus 4, and h

f prime of 5 equals the limit as x approaches 5 of the quotient of 3 times x squared minus 2 times x minus 4 minus 61, and the quantity x minus 5

limit as h approaches zero of 3 times the quantity five plus h squared minus two times the quantity five plus h minus four minus the quantity three times five squared minus two times five minus four all divided by h.

2. 

Use your graphing calculator to find the value of f '(1) for f(x) = x2 + Ln(x). (4 points)

 

1

3

2

0

3. 

How do Curves A and B compare to each other with respect to f and f ′?

Graph A increases from the left to cross the x axis near 0.6. Graph B is increasing from left to right, crossing the x axis at about 0.2, then crossing the y axis around 1, decreases to cross the x axis around 0.8 and then increasing, crossing the x axis around 1 (4 points)

 

The answer cannot be determined.

f: Curve A, f ′: Curve B, f ′′: Curve C

Neither Curve A or Curve B are derivatives of each other.

f: Curve A, f ′: Curve B

4. 

Find the equation of the line tangent to y = 2x2 - x + 4 at x = 3. (4 points)

 

y = 11x - 14

y = 4x + 14

y = 4x + 3

y = 11x + 3

5. 

If f(x) = 3a|4x - 4| - ax, where a is some constant not equal to zero, find f '(1). (4 points)

 

0

DNE

not enough information

1

1. 

Find f'(x) for f(x) = -8x2 - 5x - 4. (4 points)

 

-16x - 5

-16x - 4

16x + 5

None of these

2. 

Find f '(-3), if f(x) = (2x2 - 7x)(-x2 - 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values. (4 points)

 

3. 

Find the derivative dy, dx for y equals the quotient of the quantity x squared minus 2 times x and the quantity x cubed plus 3. . (4 points)

 

dy dx equals the quotient of the quantity 2 times x minus 2, and 3 times x squared.

dy dx equals the quotient of the quantity x cubed plus 3 times the quantity 2 times x minus 2 minus the product of x squared minus 2x and 3 times x squared, and the square of the quantity x cubed plus 3.

dy dx equals the quotient of the quantity x cubed plus 3 times the quantity 2 times x minus 2 plus the product of x squared minus 2x and 3 times x squared, and the square of the quantity x cubed plus 3.

dy dx equals the quotient of the quantity x squared minus 2 times x times the quantity 3 times x squared 2 minus the product of the quantity x cubed plus 3 times the quantity 2 times x minus 2, and the square of the quantity x cubed plus 3.

4. 

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = -5, f '(1) = -4, g '(1) = -3, g '(3) = 2, then find h '(1) if h(x) = f(x) g(x). (4 points)

 

-9

-24

0

24

5. 

Find the coefficient of the squared term in the simplified form for the second derivative, f "(x) for f(x) = (x3 + 2x + 3)(3x3 - 6x2 - 8x + 1). Use the hyphen symbol, -, for negative values. (4 points)

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1. 

If f(x) = (5x3 - 4)4, then what is f '(x)? (4 points)

 

20x2(x3 - 4)3

20x8

4(5x3 - 4)3(15x2)

4(2x3 - 4)4

2. 

Find f '(x) for f of x equals the square root of the quantity sine of 4 times x . (4 points)

 

f prime of x equals the quotient of 2 and the square root of the quantity sine of 4 times x

f prime of x equals the quotient of the cosine of 4 times x and 2 times the square root of the quantity sine of 4 times x

f prime of x equals the quotient of 2 times the cosine of 4 times x and the square root of the quantity sine of 4 times x

f'(x) = sin(8x)

3. 

Is the following true or false?

the second derivative of the quantity x squared times the cosine of x equals 2 times cosine x minus 4 times x times sine of x minus x squared times cosine x (4 points)

 

True

False

4. 

Find dy dx of y equals the cosecant of the square root of x . (4 points)

 

cotangent squared of the square root of x

the product of negative cosecant of the quantity 1 divided by 2 times the square root of x and the cotangent of the quantity 1 divided by 2 times the square root of x

the quotient of the quantity the product of negative cosecant of the square root of x and the cotangent of the square root of x, and 2 times the square root of x

product of negative cosecant of the square root of x and the cotangent of the square root of x

5. 

Differentiate y = sin2x - cos2x. (4 points)

 

2sin(x) - 2cos(x)

2sin(x) + 2cos(x)

4sin(x)cos(x)

0

1. 

If f(x) = 5x4 tan-1x, find f '(x). (4 points)

 

20x3tan-1x - 5x4tan-2x

20x3tan-1x + 5x4 1 over the square root of the quantity 1 minus x squared

20x3tan-1x - 5x4 1 over the square root of the quantity 1 minus x squared

20x3tan-1x + 5x4 1 over the quantity 1 plus x squared

2. 

Find the derivative of e6x. (4 points)

 

e6x

6xe6x

6e6x

6ex

3. 

If f(x) = ln(1 - x), then find f '(x). (4 points)

 

1 over the quantity 1 minus x

(1 - x)2

1 over the quantity 1 minus x squared

1 over the quantity x minus 1

4. 

Find the derivative with respect to x of the quantity e raised to the power of 7 times the natural log of x. . (4 points)

 

7e7lnx

the quotient of e to the 7 natural log x divided by x.

7x6

x7

5. 

For f(x) = ecos(x) use your graphing calculator to find the number of zeros for f '(x) on the closed interval [0, 2π]. (4 points)

 

1

2

3

4

1. 

Find y' if x = cos(y). (4 points)

 

-sin2(y)

sec2(y)

-tan2(y)

-csc(y)

2. 

Find dy, dx for x2 - y2 = xy. (4 points)

 

2x - 2y

2 times x divided by the quantity 1 plus 2 times y

the quantity y minus 2 times x divided by the quantity negative 2 times y minus x

0

3. 

If 3x2 + y2 = 7 then evaluate the second derivative of y with respect to x when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -, for negative values. (4 points) 

 

4. 

Find dy, dx if f(x) = (x + 8)3x. (4 points)

 

3xln(x + 8)

the product of the quantity 3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8, and the quantity x plus 8 raised to the 3x power

3 times the natural log of the quantity x plus 8 plus 3 times x divided by the quantity x plus 8

3x(x + 8)(3x - 1)

5. 

Find the slope of the graph of the relation y3 - xy = -6 at the point (7, 2). (4 points)

 

negative 2 divided by 5

2 divided by 5

negative 4 divided by 5

1 divided by 7

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