Difference Quotient

Discussion in 'Algebra' started by nycmathguy, Jul 4, 2021.

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    1,039
    Likes Received:
    208
    Find the difference quotient
    and simplify your answer.

    f(x) = x^(2/3) + 1

    [f(x) - f(8)]/(x - 8), where x cannot be 8.

    I will find f(8) first.

    Note: x^(2/3) = cuberoot{x^2}.

    cuberoot{x^2} + 1

    cuberoot{8^2} + 1

    cuberoot{64} + 1

    16 + 1 = 17

    [cuberoot{x^2} - 17]/( x - 8)

    [x^(4/3) - 289]/(x - 8)

    I don't think this can be simplified further.

    You say?
     
    nycmathguy, Jul 4, 2021
    #1
    1. Advertisements

  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    606
    Likes Received:
    594
    you are using wrong formula

    f(x) = x^(2/3) + 1

    [f(x+h) - f(x)]/ h, where h cannot be 0

    first find f(x+h)

    f(x+h) = (x+h)^(2/3) + 1
    f(x+h) = (x+h)^(2/3) + 1

    then substitute in [f(x+h) - f(x)]/ h both f(x) and f(x+h)

    [ (x+h)^(2/3) + 1 - x^(2/3) + 1]/ h

    [ (h + x)^(2/3) - x^(2/3) + 2]/ h

    or
    (h + x)^(2/3) /h- x^(2/3)/h+ 2/ h
     
    MathLover1, Jul 4, 2021
    #2
    nycmathguy likes this.
    1. Advertisements

  3. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    1,039
    Likes Received:
    208
    Understood.
     
    nycmathguy, Jul 4, 2021
    #3
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.