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Definition of a Derivative

Total questions: 15

Worksheet time: 2hrs 12mins

Name
Class
Date
1.
Derivative means the same thing as
a)
slope of the tangent line
b)
slope of the normal line
c)
exponent
d)
potato
2.
The derivative of a function is its
a)
Slope
b)
Maximum/Minimum
c)
Instantaneous rate of change
d)
Common Denominator
3.
a)

15x2

b)

(5/4)x4

c)

indeterminate

d)

4.

f'(x)=

a)

limh0(f(x+h)f(x)h)\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)

b)

limxc(f(x)f(c)xc)\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)

c)

dydx\frac{\text{d}y}{\text{d}x}

d)

an equation for the slope of the tangent line

5.

 limh0(5(x+h)25x2h)\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)  

a)

 5x25x^2  

b)

 10x10x  

c)

10

d)

DNE

6.

It's the average rate of change of y=3x^2+4x-2 on the interval [-2, 1].

a)

0

b)

1

c)

2

d)

3

7.

Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2+9 (be ready to show work on the test).

a)

x^2

b)

2x+9

c)

2

d)

2x

8.

This is NOT a correct notation for a derivative

a)

y ' (say it as "y prime")

b)

f '(x) (say it as "f prime of x")

c)

dy/dx

d)

dx/dy

9.

Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2-2x+3 (be ready to show work on the test).

a)

y ' = 2x - 2

b)

y ' = 2x^2

c)

y ' = 2x

d)

y ' = x^2

10.

Write the slope of the line tangent to the graph of y=x^2-2 at the point x = 8.

a)

2

b)

-4

c)

-8

d)

-16

11.

This is a line that touches the function at a given point and has a slope that is equal to the instantaneous rate of change at a given point.

a)

normal line

b)

tangent line

c)

delta line

d)

secant line

12.

This is the equation of the line tangent to the graph of y=x^2+3 at the point x = -1.

a)

y = -2x + 2

b)

y = 2x + 2

c)

-(1/2)x + (7/2)

d)

y = (1/2)x + (7/2)

13.
Find the slope of      y= 3x2 - 5 using the point x=2
a)
10
b)
11
c)
12
d)
13
14.
Derive                y=3x2-4x+2
a)
6x-6
b)
6x-2
c)
4-6x
d)
6x-4
15.
Find the value of the derivative at the indicated x-value.
a)
-4
b)
3
c)
0
d)
24