03 - Definition of the Derivative

[Pages:2]Kuta Software - Infinite Calculus

Name___________________________________

Definition of the Derivative

Date________________ Period____

Use the definition of the derivative to find the derivative of each function with respect to x.

1) y = -2x + 5

2) f (x) = -4x - 2

3) y = 4x2 + 1

4) f (x) = -3x2 + 4

5) y = -4x2 - 5x - 2

6) y = 3x2 + 3x + 3

7) y = -3x - 5

8) f (x) = 4x - 5

1 9) y =

x + 2

10) f (x) = - 2

2x - 1

Critical thinking question:

11) Use the definition of the derivative to show that f '(0) does not exist where f (x) = x .

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Definition of the Derivative

Date________________ Period____

Use the definition of the derivative to find the derivative of each function with respect to x.

1) y = -2x + 5

2) f (x) = -4x - 2

dy = -2

dx

f '(x) = -4

3) y = 4x2 + 1 dy = 8x dx

4) f (x) = -3x2 + 4 f '(x) = -6x

5) y = -4x2 - 5x - 2 dy = -8x - 5 dx

6) y = 3x2 + 3x + 3 dy = 6x + 3 dx

7) y = -3x - 5

dy

3

= -

dx 2 -3x - 5

8) f (x) = 4x - 5 f '(x) = 2

4x - 5

1 9) y =

x + 2

dy

1

= -

dx x2 + 4x + 4

10) f (x) = - 2

2x - 1

f

' (x)

=

4x2

-

4 4 x

+

1

Critical thinking question:

11) Use the definition of the derivative to show that f '(0) does not exist where f (x) = x .

0+h - 0

h

Using 0 in the definition, we have lim

= lim which does not exist because

h0

h

h0 h

the left-handed and right-handed limits are different.

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Worksheet by Kuta Software LLC

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