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Find the linear function with f(1) = 4 and slope 6.

Select one:

- f(x) = 4x + 6
- f(x) = 6x – 2
- f(x) = 6x + 4
- f(x) = 6x + 4x
- f(x) = 6x
^{2}– 2

The correct answer is: f(x) = 6x – 2

Question **2**

If f (t)=t^{2} + t, Between t = 10 and t = 12, what is the increase in f divided by the increase in t?

Select one:

- 2
- 46
- 23
- 1/23
- 25

The correct answer is: 23

Question **3**

If f (t)=t^{2} + t, find [ f(t + h) -f (t)]/h.

Select one:

- 2t + h + 1
- 2t + 1
- 2t
- 1
- Undefined

The correct answer is: 2t + h + 1

Question **4**

On a circle of radius R find the x and y coordinates at time t (and angle t).

Select one:

- (cos t, sin t)
- (t cos 3, t sin 3)
- (sin t, cos t)
- (Rcos t, Rsin t)
- (t cos R, t sin R)

The correct answer is: (Rcos t, Rsin t)

Question **5**

From the formula for sin (2t + t) find sin 3t in terms of sin t.

Select one:

- 3sin(t)cos(t)
- 2sin(t) + sin
^{2}(t) - sin
^{2}(t) + 3sin (t) - 6sin (t) cos (t)
- -4 sin
^{3}(t) + 3sin (t)

The correct answer is: -4 sin^{3} (t) + 3sin (t)

Which function has the same slope as g(x)= x^{2}?

Select one:

- f(x) = (1/2)x
^{2} - f(x) = 4x
^{2} - f(x) = x
^{2}+ 3 - f(x) = 2x
- f(x) = 2

The correct answer is: f(x) = x^{2}+ 3

Question **2**

What is the tangent line to f(x) = x^{2} + 3 at (4,19)?

Select one:

- y = 8x - 13
- y = -2x+ 5
- y = 4x + 19
- y = 19x + 4
- y = 2

The correct answer is: y = 8x - 13

Question **3**

What is the derivative of f(x) = (x^{2} + 1)^{2} at (3, 100)?

Select one:

- 2x
^{2}+ 2 - 120
- 100
- 2
- 3

Question **4**

The tangent line to y = x^{3} + 6x at the origin is?

Select one:

- y = 3x + 6
- y = 3
- y= 6
- y = 6x + 3
- y = 6x

The correct answer is: y = 6x

Question **5**

What is Lim (t^{2} - 4) / (t – 2)

t→2

Select one:

- 0
- 2
- 4
- 6
- Undefined

The correct answer is: 4

What is the derivative of f(x) times g(x), if f(x) = 2x + 1 and g(x) = x^{2}?

Select one:

- (1/2)x
^{2} - 6x
^{2}+ 2x - 8x
- 8
- 0

Question **2**

What is the derivative of f(x) divided by g(x), if f(x) = 2x + 1 and g(x) = x^{2}?

Select one:

- -2/x
^{2}- 2/x^{3} - 6x
^{2}+ 2x - 2x
^{2}+ 3 - 0
- Impossible

Question **3**

What is the derivative of f(x) = -cos x?

Select one:

- -cos x
- cos x
- sin x
- -sin x
- 0

Question **4**

The tangent line to y = 3 sin x + 2 at (pi, 2) is:

Select one:

- y = 3x + 6
- y = -3x +5
- y= -3
- y = -3x -6
- y = -3x + 3pi +2

Question **5**

Why is f(x) = { 5 for x >0

3 for x = 0

5 for x < 0

not continuous at x = 0?

Select one:

- Because f(x) is not defined at x = 0
- Because f(x) is not differentiable at x = 0
- Because the left hand limit does not equal the right hand limit as x goes to 0
- Because f(0) does not equal both (or either) the left hand limit and/or the right hand limit
- It is continuous at x = 0

What is the derivative of f(x) = 5xe^{3x} at the point (0, 0)?

Select one:

- 0
- 5
- 10
- 15
- 3

Question **2**

What is the tangent line to f(x) = (e^{z} +3)^{2} at (0, 16)?

Select one:

- y = -6x + 16
- y = 6x + 16
- y = 16
- y = 6x + 9
- y = 2

Question **3**

What is the derivative of f(x) = ln (3x +1)?

Select one:

- f’(x) = 3 / (3x + 1)
- f’(x) = 1/(3x + 1)
- f’(x) = 3/ (ln (3x + 1))
- f’(x) = 1/ (ln (3x+ 1))
- Impossible

Question **4**

How long will it take $10,000 to compound continuously to $30,000 at 7% interest? Choose the closest answer.

Select one:

- About 5 years
- About 10 years
- About 15 years
- About 20 years
- Never

Question **5**

The half life of Carbon-14 is 5,730 years (i.e., it decays so that only have remains after 5,730 years). How long until 16 grams of Carbon-14 decays into 4 grams?

Select one:

- 1,000 years
- 5,730 years
- 11,460 years
- A million years
- Undefined

What is the linear approximation to f(x) = sin x, , near x = pi/2?

Select one:

- y =cos x
- y = 0
- y = 1
- y = pi/2
- y = pi/2 + 1

The correct answer is: y = 1

Question **2**

The local maximum of f(x)=x^{3} - 9x occurs at what value of x?

Select one:

- 0
- 3
- -3
- the square root of 3
- –(the square root of 3)

The correct answer is: –(the square root of 3)

Question **3**

Where is f(x) = x^{3} - 6x^{2} concave down?

Select one:

- (-infinity, 2)
- (2, infinity)
- (-infinity, infinity)
- (-2, 2)
- (-infinity, -2)

The correct answer is: (-infinity, 2)

Question **4**

Find all points 0 <c <2 where f (2) -f (0) =f '(c)(2 -0), for f(x)= 1 +x+x^{2}.

Select one:

- c =3
- c =2
- c = 1
- c =0
- There are no such points

The correct answer is: c = 1

Question **5**

What is Lim (x – pi) / (sin x)?

t→pi

Select one:

- 1
- 0
- -1
- Infinity
- Undefined

The correct answer is: -1

What is the derivative of f(x) = (x + sin x)^{3}?

Select one:

- f’(x) = 3(1 + cos x)
^{2} - f’(x) = 3(1 + sin x)
^{2} - f’(x) = 1 + cos x
- f(x) = 3(1+ cos x)(x + sin x)
^{2} - Impossible

The correct answer is: f(x) = 3(1+ cos x)(x + sin x)^{2}

Question **2**

What is the tangent line to f(x) = (x^{3} + 3x – 5)^{4} at (1,1)?

Select one:

- y = -24x + 25
- y = 25x -24
- y = 1x + 1
- y = 1
- Impossible

The correct answer is: y = -24x + 25

Question **3**

What is the derivative of f(x) = (x^{2} + 1)^{2} at (3, 100)?

Select one:

- 2x
^{2}+ 2 - 120
- 100
- 2
- 3

Question **4**

If x^{2} y + xy^{2} = 1, what is y’?

Select one:

- y’ = 0
- y’ = -1/2x
- y’ = (-2xy – x
^{2}) / (y^{2}+ 2xy) - y’ = (y
^{2}+ 2xy) / (-2xy – x^{2}) - y’ is undefined

The correct answer is: y’ = (y^{2} + 2xy) / (-2xy – x^{2})

Question **5**

Consider the circle x^{2} + y^{2} = 9. What is the tangent line to this circle at (3, 0)?

Select one:

- y =0
- x = 3
- y = x
^{2}- 9 - x = 0
- Undefined

The correct answer is: x = 3

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