1. If f(x) =\frac{x^2+1}{x^2-1}, find the value(s) of x where the graph of f has a horizontal...


1. If {eq}f(x) =\frac{x^2+1}{x^2-1}, {/eq} find the value(s) of x where the graph of {eq}f {/eq} has a horizontal tangents.

2. Prove the quotient rule using the product rule and the chain rule.

3. Simplify the following expression in terms of a derivative

lim{eq}_{h\rightarrow0}\frac{g(7+h)-g(7)}{h}= {/eq}

Rational Functions

When we investigate a rational expression or function we need the quotient rule for the derivatives.

A quotient is zero, if and only if its numerator is zero. The numerator will be a polynomial and

we have a formula up to degree two polynomials.

Answer and Explanation:


We need to find the points where the slope is zero. In other words, the critical points

{eq}\begin{align*} f'(x) &= 0...

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Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4

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