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Unit 5 Day 4 & 5 Derivatives Review

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  • Unit 5Day 4 & 5

    Derivatives Review

  • Warm Up: (Review Day)

    1. Using the limits definition of derivatives, find the derivative of f(x) given below: Simplify your answer.

    2. Find the equation of the tangent line to at x = 3. Write the

    line in slope intercept form.

    3 213 56 83y x x x

    ( ) 7f x x

  • Warm Up: (Review Day)

    1. Using the limits definition of derivatives, find the derivative of f(x) given below: Simplify your answer. ( ) 7f x x

  • Warm Up: (Review Day)

    2. Find the equation of the tangent line to

    at x = 3. Write the line in slope intercept form.

    3 213 56 83y x x x

  • Warm Up: (Review Day) ANSWERS

    1. Using the limits definition of derivatives, find the derivative of:Simplify your answer.

    2. Find the equation of the tangent line to at x = 3. Write the

    line in slope intercept form.

    3 213 56 83y x x x

    5 5( 3)y x

    1'( )

    2 7f x

    x

    5 20y x

    ( ) 7f x x

  • Homework Questions?!

  • Tonight’s Homework

    • Finish MATHO (Packet p. 6)

    • Quiz Review sheet

    • Study for Quiz!

  • Check-In: On NEW notebook paper

    1. Using the limits definition of derivatives, find the derivative of f(x) given below.

    Using the Chain Rule, find the derivative of g(x), given below. Express answers with positive whole exponents and radicals.

    2.

    3.

    3( ) 2 4 3g x x x

    ( ) 68

    xg x x

    When done:1) Turn in paper to

    Blue Basket by door. 2) Start Packet p. 6

    problems.

    2( ) 4 2f x x x

  • MATHO

  • Practice: (Review Day)

    1. Using the limits definition of derivatives, find the derivative of f(x) given below: Simplify your answer. f (x) =

    2

    x - 4

  • Practice: (Review Day) ANSWERS

    1. Using the limits definition of derivatives, find the derivative of f(x) given below.Simplify your answer.

    f (x) =2

    x - 4

    2

    2'( )

    8 16f x

    x x

  • a) Find the equation of the line tangent to

    November 3, 2017 12

    3 22 4 2y x x x at x

    Warm Up (Quiz Day)

    24 6 2 3y x x at x

    b) Find the equation of the line tangent to

    c) Use the limit definition to find the derivative of and 2( )

    3f x

    x

    ( ) 3g x x

  • a) Find the equation of the line tangent to

    November 3, 2017 13

    3 22 4 2y x x x at x

    Warm Up (Quiz Day) ANSWERS

    24 6 2 3y x x at x

    b) Find the equation of the line tangent to

    c) Use the limit definition to find the derivative of and 2( )

    3f x

    x

    ( ) 3g x x

    34 41( 2)

    41 48

    y x

    y x

    52 30( 3)

    30 38

    y x

    y x

    2

    2'( )

    6 9f x

    x x

    1'( )

    2 3g x

    x

  • Unit 5Whiteboard Quiz Review

    Derivatives

  • What is the limit definition of a derivative?

    0

    ( ) ( )limh

    f x h f x

    h

  • Find the derivative using the limit definition of derivatives.

    f (x) = 2x-4

    '( ) 2f x

  • Find the derivative using the power rule. Write your answer with positive, whole

    exponents or radicals.

    4( ) 4 5 2 3f x x x x

    3 1'( ) 16 5f x xx

  • Find the slope of the functionat x = 9.2 12 5y x x

    20m

  • Find the derivative of the function.

    ' 2y

  • Find the derivative using the limit definition of derivatives.

    g(x) = x2 -5x+6

    '( ) 2 5g x x

  • Find the derivative using the power rule.Write answers with positive, whole

    exponents or radicals.

    53

    5 3

    4 2( )f x x

    x x

    3 2

    6 4

    20 6 5'( )

    3

    xf x

    x x

  • Find the equation of the line tangent topoint at (3, 2).y = x3 -3x2 +2

    2 9( 3)

    9 25

    y x

    or y x

  • Find the slope intercept equation of the tangent line of when x = 2

    2( ) 5 3 7g x x x

    17 13y x

  • Find the derivative using the limit definition of derivatives.

    1'( )

    2 2h x

    x

    h(x) = 2+ x

  • Find the equation of the line tangent topoint at (2, 2).y = x3 -2x2 +2

    2 4( 2)

    4 6

    y x

    or y x

  • Find the derivative using the limit definition of derivatives.

    h(x) =2

    x+3

    2 2

    2 2'( )

    6 9 ( 3)h x

    x x x

  • Find the derivative using the power rule.

    f (x) = x2

    3

    1 3

    3

    2 2'( )

    33

    f x ORx

    x

  • Find the derivative of the functionat x = -1.y = -x3 +3x2 +3

    f '(x) = -9

  • Find the derivative using the power rule.

    g(x) = -1

    2x4 +3x

    5

    3 + 2x

    2

    3 3'( ) 2 5 2g x x x

  • MATHO

  • Homework

    • Finish MATHO Packet p. 6

    • Quiz Review sheet

    • Study for Quiz!


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