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Lesson 51: Derivatives of Polynomial Functions
A quick review of the symbols that represent the derivative
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Leibniz Notation:
,
Prime Notation:
For example, the derivative of y = 3x2 (which can also be written as f(x) = 3x2 )
is 6x
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1
Derivative Rules:
Although we may have noticed some patterns in the last unit when taking
derivatives of polynomial functions, we need to prove that these patterns work
all the time
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So far, all we have is the definition of a derivative from the last unit
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Constant Rule:
Proof:
Example: Find the derivative of f(x) = 7
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The power rule does work for all ,
but that will have to be left for university calculus
Example: Find the derivative of y = x5
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4
Sum & Difference Rule:
Proof of the Sum Rule:
The proof of the difference rule is similar
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5
Example: Find the derivative of each
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9t2 + 20t + 2
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0 s?
At what time is the object stopped?
c)
At what point in its flight is the object stopped?
d)
At what time does the object hit the ground?
7