03 - Definition of the Derivative
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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