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Applied Calculus (MAT 121) Dr. Day Thursday Feb 2, 2012. Review Meaning and Definition of the Derivative (2.6) Shortcut Rules for Determining Derivatives (3.1 ) Applications Requiring Use of Derivatives (2.6, 3.1) Derivatives of Products and Quotients (3.2) Assignments & Test #1 Results.

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Applied calculus mat 121 dr day thursday feb 2 2012
Applied Calculus (MAT 121)Dr. Day Thursday Feb 2, 2012

Review

  • Meaning and Definition of the Derivative (2.6)

  • Shortcut Rules for Determining Derivatives (3.1)

  • Applications Requiring Use of Derivatives (2.6, 3.1)

  • Derivatives of Products and Quotients (3.2)

  • Assignments & Test #1 Results

  • MAT 121


    Review limits and derivatives
    Review: Limits and Derivatives

    • What do we mean when we say we are “determining the limit of a function at a point?”

      • Show a graphical and a numerical example to illustrate this.

      • Write a sentence or two to tie it all together.

    • What is our purpose in determining the derivative of a function? Why bother?

    • State the formal definition for the derivative of a function f(x).

    MAT 121




    Review shortcuts for determining derivatives 3 1
    Review: Shortcuts for Determining Derivatives (3.1)

    MAT 121


    Shortcut rules for determining derivatives 3 1
    Shortcut Rules for Determining Derivatives (3.1)

    • What if the function is a constant function? y = k

    • What if the function is a power function? y = xn

    • What if the function includes a coefficient? y = cf(x)

    • What if the function is the sum or difference of several functions? y = cf(x) + dg(x)

      Applications of Derivatives

    MAT 121


    Shortcut rules for derivatives 3 1
    Shortcut Rules for Derivatives (3.1)

    • What if the function is a constant function? y = k

    • The derivative of any constant function is 0:

      If y = f(x) = k, then y’ = f’(x) = 0

    MAT 121


    Shortcut rules for derivatives 3 11
    Shortcut Rules for Derivatives (3.1)

    • What if the function is a power function? y = xn

      If y = f(x) = xn, then y’ = f’(x) = nxn-1.

    MAT 121


    Shortcut rules for derivatives 3 12
    Shortcut Rules for Derivatives (3.1)

    • What if the function includes a coefficient? y=cf(x)

      If y = cf(x), then y’ = cf’(x).

    MAT 121


    Shortcut rules for derivatives 3 13
    Shortcut Rules for Derivatives (3.1)

    • What if the function is the sum or difference of several functions? y=cf(x) + dg(x)

      If y = cf(x) + dg(x), then y’ = cf’(x) + dg’(x).

    MAT 121


    Derivatives of products 3 2
    Derivatives of Products (3.2)

    If y = h(x) = f(x)g(x), then

    y’ = h’(x) = f’(x)g(x) + f(x)g’(x)

    The derivative of a product of two functions is:

    The derivative of the first times the second

    plus

    the first times the derivative of the second.

    MAT 121


    Derivatives of quotients 3 2
    Derivatives of Quotients (3.2)

    If:

    Then:

    The derivative of a quotient of two functions is:

    The derivative of the top times the bottom

    minus

    the top times the derivative of the bottom

    All over

    The bottom squared.

    MAT 121


    Assignments
    Assignments

    WebAssign

    • 3.1 tonight

    • 3.2 Friday night

    MAT 121


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