calculus (derivativs)

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Find the points on the graph of f where the tangent line is horizontal.

original: x/x^2+25)

After I did the quotient rule I got:

(x^2+25)(1)-(x)(2x)/((x^2+25))^2

Then of course I know you set that equal to 0, but I do not know how to set it up or "finalize" the problem because of the denominator. Please help!

  • calculus (derivativs) -

    ((x^2+25)(1)-(x)(2x))/(x^2+25)^2 = 0

    Simplify
    (25-x^2)/(x^2+25)^2 = 0

    As long as x^2+25 <> 0 then you can multiply both sides by the denominator

    (25-x^2) = 0

    Thus
    x^2 = 25
    x = ±5

    ( Check: 25+25<>0 .. okay)

    Find y when x=-5 and x=+5. These are your points

  • calculus (derivativs) -

    does that go into the derivative equation or the original?

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