Fractional Powers Differentiation practice problem

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freelandjeffrey

15. december 2016 04:26

While doing the practice problems for differentiation with fractional powers, I ran across one where I'm given f(x) = 3x^(1/2), and I'm supposed to find f'(4). I followed the rules, getting f'(x) = 3/(2*x^(1/2)). Putting in 4, I get 3/4 as my answer, which is what the problem also said the answer was. Graphing f(x) appears to agree with this result.

But when I square root, don't I need to add + or - ? Algebraically, it seems I'd end up with plus or minus 3/4. If I didn't have access to a graph, how would I know which is correct? Would I have to just evaluate f(x) for a couple values around 4 and see if it's increasing or decreasing?

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Kyle Riggs

15. december 2016 19:57
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I had the same question a little bit ago but a very good teacher taught me that since the question asked for the positive square root ( also called the Principal Square root), you only need to worry about the positive side.

The definition of the principal squareroot symbol √ means the domain of the result is positive or 0.

So in your question because the symbol in the question was most likely d/dx [√(3x)] then when evaluating f'4, you only take +2 and not -2 because √ = +√

Hope this helps.

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Fractional Powers Differentiation practice problem

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