(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the derivative of f using the differance quotient and use the derivative of f to determine any points on the graph of f where the tangent line is horizontal.

[tex]f(x)=3x^3-9x[/tex]

2. Relevant equations

3. The attempt at a solution

[tex]\lim_{\Delta x\rightarrow0}=\frac{3(x+\Delta x)^3-9(x+\Delta x)-3x^3+9x}{\Delta x}[/tex]

[tex]\lim_{\Delta x\rightarrow0}=\frac{3(x^3+3x^2\Delta x+3x\Delta x^2+\Delta x^3)-9x-9\Delta x-3x^3+9x}{\Delta x}[/tex]

[tex]\lim_{\Delta x\rightarrow0}=\frac{3x^3+9x^2\Delta x+9x\Delta x^2+3\Delta x^3-9x-9\Delta x-3x^3+9x}{\Delta x}[/tex]

The '3x^{3}'s and '9x's cancel out and you are left with

[tex]\lim_{\Delta x\rightarrow0}=\frac{9x^2\Delta x+9x\Delta x^2+3\Delta x^3-9\Delta x}{\Delta x}[/tex]

Then if you take the limit as delta x approaches 0 you will get

[tex]9x^2+9x-6[/tex] I know the answer is [tex]9x^2-9[/tex] via the rules of differentiation.

What am I doing wrong with this example?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Difference Quotient Isn't working.

**Physics Forums | Science Articles, Homework Help, Discussion**