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www.clutchprep.com CALCULUS - CLUTCH CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
FIRST DERIVATIVE TEST
● First derivative tells us when f(x) _____________ & _____________.
● Critical numbers are the _________________ of the .
●A maximum is a change from _________ to _________ in the .
●A minimum is a change from _________ to _________ in the
EXAMPLE 1: Given
A) Find the critical numbers, B) Find the intervals when is increasing & decreasing,
C) Find the extreme values,
EXAMPLE 2: Given
A) Find the critical numbers,
B) Find the intervals when is increasing & decreasing,
C) Find the local & absolute extreme values,
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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PRACTICE: FIRST DERIVATIVE TEST
PROBLEM: Compute the first derivative test.
Given ( ) find the intervals when ( ) is increasing.
A ( )
B ( )
C ( )
D ( ) ( )
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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PROBLEM: Compute the first derivative test
Given ( ) determine the extremas of ( ).
A Local max at
B Local min at
C Local max at
D Local min at
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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SECOND DERIVATIVE TEST
● Second derivative tells us when ____________ & ____________.
● Points of Inflection come from the _________________ of .
● They occur when changes _________________( ) .
● is concave up when is ______________.
● is concave down when is ______________.
EXAMPLE 1: Given
A) Find the intervals when is concave up & concave down,
B) Find the points of inflections,
EXAMPLE 2: Given
A) Find the intervals when is concave up & concave down,,
B) Find the points of inflections,
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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PRACTICE: SECOND DERIVATIVE TEST
PROBLEM: Compute the second derivative test.
Given ( ) find the points of inflections of ( ) ?
A
B ⁄
C ⁄
D
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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CURVE SKETCHING (Part 1)
● We put everything together to be able to sketch a function.
EXAMPLE 1: Sketch the curve of ( )
a)
e+f) f)
b)
c)
h)
d)
Check Box
(a) Domain (b) Intercepts (c) Symmetry
(d) Asymptotes (e) Local Max & Local Min
(f) Interval of Increase or Decrease (g) Concavity and Points of Inflection
(h) Sketch the graph
g)
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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CURVE SKETCHING (Part 2)
● We put everything together (check box) to be able to sketch a function.
● With rational functions look out for where the derivatives is undefined.
EXAMPLE 1: Sketch the curve of
a)
e+f) f)
b)
c)
h)
d)
Check Box
(a) Domain (b) Intercepts (c) Symmetry
(d) Asymptotes (e) Local Max & Local Min
(f) Interval of Increase or Decrease (g) Concavity and Points of Inflection
(h) Sketch the graph
g)
CALCULUS - CLUTCH
CH.9: APPLICATIONS OF DERIVATIVES (PART 2)
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