Free Printable More Calculus

1.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

2.

Find f '(2) if
f(x) = x² + 2x

a)

2x + 2

b)

6

c)

12

d)

2x

3.

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

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

4.

Find the slope of f(x) = -3x² – 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

5.

Find the derivative of
$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$

a)

$-2x^2-x+9$

b)

$-2x^3-x^2+9x$

c)

$-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$

d)

$-2x^4-x^3+9x^2$

6.

the derivative is...

a)

slope of the secant line

b)

slope of the tangent line

c)

slope of the cosecant line

d)

slope of the normal line

7.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

8.

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

a)

y+1=2(x+1)

b)

y=2x-1

c)

y=2x+2

d)

y= -x-1

9.

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

10.

If f '(x) = 0, what does that mean with respect to the tangent line?

a)

Tangent line is vertical

b)

Tangent line has a positive slope

c)

Tangent line is horizontal

d)

Tangent line has a negative slope

11.

Which of the following means "first derivative"

a)

f'(x)

b)

y'

c)

dy/dx

d)

all of the above

12.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

13.

What is the slope of the line normal to the curve y = x² + x at x = 1?

a)

-1

b)

-1/2

c)

-1/3

d)

-1/4

14.

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)

$y=2x$

15.

Write the equation of the normal line of: $f\left(x\right)=2x^2-\frac{1}{x}$ at x = 1

a)

$y=-\frac{1}{5}x+\frac{4}{5}$

b)

$y=5x-6$

c)

$y-1=5\left(x-1\right)$

d)

$y-1=-\frac{1}{5}\left(x-1\right)$

16.

Find the equation of the normal line at x = 0 of:
$f\left(x\right)\ =\ x^3+e^x$

a)

$y=-x+1$

b)

$y=\ x+1$

c)

$y=-x\ -1$

d)

$y=x\ -\ 1$

17.

Where is the decreasing?

a)

( −∞, −2.55) U (0, 2.55)

b)

(∞, −6.25) U (36, −6.25)

c)

(−∞, ∞)

d)

(−∞, 0)

18.

Calculate the derivative of f(x)= 3x⁴-7x²+8x

a)

12x⁵-7x³+8x²

b)

12x⁴-14x²+8x²

c)

12x³-14x+8

d)

3x³-7x²+8

19.

Which are the intervals for the graph?

a)

Dec: (-∞, 3)∪(4.5, -6)

Inc: (3, 4.5) ∪ (-6, ∞)

b)

Inc: (-∞, -2)∪(-1, 1)

Dec: (-2, -1) ∪ (1, ∞)

c)

Inc: (-∞, -2) Dec: (-2, ∞)

d)

Dec: (-∞, -2)∪(-1, 1)

Inc: (-2, -1) ∪ (1, ∞)

20.

Find the critical points of f(x) = 2x⁴- 4x² + 1

a)

x= 0

b)

x = -1, 1

c)

x = -1, 0, 1

d)

no critical points

21.

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

a)

decreasing

b)

increasing

c)

concave up

d)

concave down

22.

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

23.

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

a)

an inflection point

b)

a critical point

c)

a relative maximum

d)

a relative minimum

24.

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

25.

f' is given, which could be f?

a)

A

b)

B

c)

C

More Calculus

Total questions: 25

Worksheet time: 6hrs 15mins

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