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Section 1.4 – Difference Quotient

Section Details.
  • Definition of the diffence quotient
  • Evaluating the difference quotient for a function and simplifying the answer


Practice Problems


Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
  1.  Compute the difference quotient for \(\displaystyle{ f(x) = \dfrac{x}{2x+1}}\).

    DQ \( = \dfrac{1}{(2x+1)(2(x+h)+1)}\)

    To see the full video page and find related videos, click the following link.
    WIR7 20B M150 V13


  2. Compute the difference quotient for \(\displaystyle{ g(x) = \sqrt{3x-7}}\).

    DQ \( = \dfrac{3}{\sqrt{3x+3h-7}+\sqrt{3x-7}}\)

    To see the full video page and find related videos, click the following link.
    WIR7 20B M150 V14


  3. Compute the difference quotient for \(f(x)=\displaystyle \frac{x}{x+1}\).

    DQ \( = \displaystyle \frac{1}{(x+1)(x+h+1)}\)

    To see the full video page and find related videos, click the following link.
    WIR8 20B M150 V15