Free Printable Review for Basic Calculus

1.

How many derivatives can you take of a function?

a)

only 3

b)

only 2

c)

only 1

d)

until you can no longer derive it

2.

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

a)

7

b)

0

c)

7x

d)

14

3.

Find the derivative of the given equation
f(x) = -4x

a)

4

b)

x

c)

-4

d)

0

4.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

5.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

6.

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

a)

y = 500x + 400

b)

y = 100x + 400

c)

y = -500 x - 400

d)

y = 500x - 400

7.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

a)

(12x³)*(10x)

b)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

c)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

8.

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

9.

Find the second derivative of the following functions with respect to x.
y=3x²+5x-1

a)

6x+5

b)

3x+5

c)

5

d)

6

10.

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

a)

200x³+36x²-30x+4

b)

600x² +72x -26

c)

600x² +72x -30

d)

600x² +72x -36

11.

Find the 2nd derivative of f(x) = ¾x^½

a)

3/4x^-3/2

b)

⅛x^-½

c)

-1/16x^-½

d)

-1/16x^-3/2

12.

Find the second derivative of the following functions with respect to x.
y=(x³+x)/x²

a)

x+(1/x)

b)

1-(1/x²)

c)

2/x²

d)

2/x³

13.

Find y'' for y = 3x² + 5x + cos x

a)

f''(x) = 6x + cos x

b)

f''(x) = 3x + 5 - sin x

c)

f''(x) = 6x + 5 + sin x

d)

f''(x) = 6 - cos x

14.

What is f''(x) if f(x) = cos(5x⁴)?

a)

f''(x) = $-120x^5\cos\left(5x^4\right)$

b)

f''(x) = $-20x^3\sin\left(5x^4\right)$

c)

f''(x) = $-20x^3\cos\left(5x^4\right)\ -60x^2\sin\left(5x^4\right)$

d)

f''(x) = $-400x^6\cos\left(5x^4\right)\ -60x^2\sin\left(5x^4\right)$

15.

Find the second derivative (by Implicit Differentiation) of

8x² + 16y² = 144 at (1,1).

a)

$\frac{3}{4}$

b)

$\frac{-3}{4}$

c)

$\frac{1}{4}$

d)

$\frac{-1}{4}$

16.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

slope of the secant line

d)

the function’s value

17.

When we "take the derivative" of a function what are we finding?

a)

What's a derivative?

b)

The rate at which our struggles in Calculus are increasing.

c)

The slope of the secant line

d)

The slope of the tangent line

18.

Find the slope at x = 3 of the equation f(x) = 3x²

a)

6x

b)

27

c)

18

d)

3x

19.

Find the slope of the Normal line to: $f\left(x\right)\ =\ \frac{4\sqrt{x}}{5}$
at x = 16

a)

$\frac{2}{5}$

b)

$-\frac{1}{160}$

c)

$\frac{1}{10}$

d)

$-10$

20.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

21.

What is the derivative of f(x)= cx?

a)

c

b)

x

c)

1

d)

0

22.

Differentiate y= x³ + 2x

a)

3x³+2x

b)

3x²+2

c)

3x+2

d)

3x

23.

What is the derivative of a constant, C?

a)

C

b)

1

c)

0

24.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

25.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

26.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

27.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

28.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

29.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

Review for Basic Calculus

Total questions: 29

Worksheet time: 1hrs 19mins

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