Free Printable Calculus Unit 3 Review

1.

A derivative is the ____ of an object after a certain amount of time.

a)

Acceleration

b)

Speed

c)

Distance

d)

Height

2.

The second derivative of an equation is the ___ of an object after a certain amount of time.

a)

Acceleration

b)

Distance

c)

Speed

d)

Height

3.

$f\left(x\right)=4x^3-12x^2+6x-3$ Find the derivative of the equation.

a)

$12x^2-24x^2+6$

b)

$12x^3-24x^2+6$

c)

$12x^2+24x+6$

d)

$12x^2-24x+6$

4.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

5.

Find the derivative of the given equation
f(x) = $\frac{1}{x^2}$ Hint: rewrite with a negative exponent

a)

f'(x) = 1/2x

b)

f'(x) = -2x^-3

c)

f'(x) = 2x

d)

f'(x) = -2x

6.

Which of the following stand for the term "derivative?"

a)

d/dv

b)

d/dx

c)

f(x)

d)

f'(x)

7.

What is the formula of a derivative?

a)

f(x)=n(x)^(n-1)

b)

f(x)=x(n)^(x-1)

c)

f'(x)=n(x)^(n-1)

d)

f'(x)=x(n)^(x-1)

8.

Use product rule to find the derivative.

f(x)=(3x-1)(2x^2+1)

a)

(fg)'=(3)(4x)-(3x-1)(2x^2+1)

b)

(fg)'=(3)(2x^2+1)+(3)(4x)

c)

(fg)'=(3)(2x^2+1)+(3x-1)(4x)

d)

f'(x)=(3)(2x^2+1)+(3x-1)(4x)

9.

What is the derivative of a function inside of the equation of a tangent line?

a)

The slope

b)

The x

c)

The y

d)

The exponent

10.

What is the formula of the quotient rule?

a)

(f/g)'= [(g)(f)-(f)(g)]/(g)^2

b)

(f/g)'=[(g)(f')-(f)(g')]/(g)^2

c)

(f/g)'= [(g)(f')-(g)(f')]/(g)^2

d)

(f/g)'= [(f)(g')-(f)(g')]/(g)^2

11.

Can you find the derivative of an equation that is not a function?

a)

Yes

b)

No

12.

What is the difference between the product and quotient rules?

a)

Q = (x)*(x) | P = (x)/(x)

b)

Q = (x)/(x) | P = (x)/(x)

c)

P = (x)*(x) | Q = (x)/(x)

d)

P = (x)*(x) | Q = (x)*(x)

13.

Which of the following are true rules of derivatives?

a)

Product Rule

b)

Triple Product Rule

c)

Quotient Rule

d)

Chain Rule

14.

Solve for the derivative.

f(x)=ln(4x)

a)

f'(x) = 1/4x

b)

f'(x) = 4/x

c)

f'(x) = (1/4x) (4)

d)

f'(x) = (4/x) (x)

15.

What would the following be an example of?

(x + 1)(4x^2 - 5)

a)

Product Rule

b)

Quotient Rule

c)

Chain Rule

d)

Natural Log Rule

16.

Find the derivative of the equation.

2y^2 = 4x

a)

y' = 4x/8y

b)

y' = 2x/4y

c)

y = 4x/4y

d)

y' = 4x/4y

17.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

18.

Find $\frac{dy}{dx}$ : $y^2=20x$

a)

$\frac{5}{y}$

b)

$\frac{10}{y}$

c)

$\frac{y^2}{5}$

d)

$\frac{y^2}{10}$

19.

What is dy/dx if

5x^2y^3\ =\ 12

a)

$\frac{dy}{dx}=-\frac{2y}{3x}$

b)

$\frac{dy}{dx}=-\frac{2x}{3y}$

c)

$\frac{dy}{dx}=\frac{2y}{3x}$

d)

$\frac{dy}{dx}=-\frac{3x}{2y}$

20.

$C\left(q\right)=810+3q+0002q^2$ is the equation of the weekly cost, in dollars, for producing q lamps.

Find the number of lamps that should be produced in order to minimize the average cost.

a)

q = 642

b)

q = 636

c)

q = 572

d)

q = 596

21.

$C\left(q\right)=16,000+500q-1.6q^2+0.004q^3$ $p=1700-7q$
For the cost and price functions given, find the value of q that will maximize profit.

a)

q = 112

b)

q = 171

c)

q = 98

d)

q = 109

22.

Which of the following terms are used in cost functions?

a)

Fixed Costs

b)

Average Costs

c)

Minimize Costs

d)

Maximize Profit

e)

Marginal Revenue

23.

What is the equation of the tangent line at x = 1 $of$ $f\left(x\right)=\ \sqrt{x}$

a)

$y=\frac{1}{2}x-\frac{1}{2}$

b)

$y=\frac{1}{2}x+\frac{1}{2}$

c)

$y=2x-1$

d)

$y=2x$

24.

Find the equation of the tangent line at the point (-1,1) of: $f\left(x\right)\ =\ x^4$

a)

$y=-\frac{1}{4}x-3$

b)

$y=-4x-3$

c)

$y=\frac{1}{4}x+3$

d)

$y=4x+3$

25.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

Calculus Unit 3 Review

Total questions: 25

Worksheet time: 31mins

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