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Derivatives
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Home
/
Calculus
/
Derivatives
/
Exercises
/
The Derivative Function Exercises
TABLE OF CONTENTS
Intro
Topics
Examples
Exercises
Slope of a Line Between Two Points
Slope of a Line Between Two Points on a Function
Slope at One Point?
Estimating Derivatives from Tables
Finding Derivatives Using Formulas
Average Rate of Change
Units, Words, and Notation
How Tangent Lines Look
When Tangent Lines Don't Exist
Tangent Lines and Derivatives
Finding Tangent Lines
Differentiability and Continuity
The Derivative Function
Graphs of
f
(
x
) and
f
' (
x
)
Rolle's Theorem
The Mean Value Theorem
Quizzes
Terms
Handouts
Best of the Web
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Example 1
Let
f
(
x
) =
x
^{3}
. Use the formula we found
for
f'
(
x
) to evaluate
f
'(4)
Show Answer
Answer
f
'(4) = 3(4)
^{2}
= 48
Example 2
Let
f
(
x
) =
x
^{3}
. Use the formula we found
for
f'
(
x
) to evaluate
f
'(-5)
Show Answer
Answer
f
'(-5) = 3(-5)
^{2}
= 75
Example 3
Let
f
(
x
) =
x
^{3}
. Use the formula we found for
f'
(
x
) to evaluate
Show Answer
Answer
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