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

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

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

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

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

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