Question

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!

Answer 1

((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

Answer 2

does that go into the derivative equation or the original?