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

I'm having trouble factoring this to its simplest term. I'm not very good at factoring, but I'm working on it. I was hoping that someone might be able to help me here.

2. Relevant equations

Find the critical points for f(t) = t * sqrt(4 -(t^2)) on the closed interval [1, -2].

3. The attempt at a solution

Using the product rule, this is where I'm at:

f'(t) = ((4 - (t^2))^(1/2)) + ((t^2)*((4 - (t^2))^(-1/2))).

I want to reduce this down so as to make it easier to set the equation to 0 to find the critical points.

My question is, how can I factor this down to its simplest terms? I see some common terms in the answer, I'm just not sure what of process to use to reduce it?

If there is any confusion in my notation, then please let me know. I tried to use parenthesis as liberally as possible so to make the arithmetic operations clear.

By the way, in case you wanted to check your solution, the book has f(sqrt(2)) = 2 and f(-1) = -sqrt(3) as the critical points.

I really appreciate the help.

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# Homework Help: Simple factoring after differentiating.

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