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

I am given the following function:

[tex]f(x)=\frac{2x^2}{x-1}[/tex]

The question asks to find the critical points and classify each using the second derivative.

2. Relevant equations

3. The attempt at a solution

I got the derivative of f(x) to be:

[tex]f'(x)=\frac{2x^2-4x}{(x-1)^2}[/tex]

So the critical points are when x=0, x=1, and x=2.

Here's where I'm stuck. I don't know what it means when it asks to classify each using the second derivative.

If it helps, the second derivative is:

[tex] f''(x)=\frac{-8x^2+12x-4}{(x-1)^4}[/tex]

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# Homework Help: Curve Sketching with Derivatives?

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