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I have a question that I would just like a little bit of clarification about.

Find a and b, 0 < a 1, 0 < b 1 such that max x is element of [−1,1] |(x + b)(x + a)(x − a)(x − b)| = max x is element of [−1,1] |(x2 − a2)(x2 − b2)| be as small as possible.

In class my teacher said that Si(x) = 2x(x^2-a^2) + 2x(x^2-b^2) = 0.

I know why we set it equal to zero but where does the left side of the equation come from? I cannot figure this out and would appreciate any help!


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Please check the question text again, it would help if you could make it more clear. – NoChance Sep 10 '12 at 1:46
up vote 0 down vote accepted

Use the product rule. Let f(x) = x^2 - a^2 g(x) = x^2 - b^2 Then f'(x) = 2x g'(x) = 2x Thus (f(x)g(x))' = 2x(x^2-a^2) + 2x(x^2-b^2)

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