Expert: Paul Klarreich - 12/10/2009

Question
Find all the points at which the tangent line to the curve is horizontal.

f(x) = square root of x

I rewrote the function as (x)^1/2 and then found the derivative, which was 1/2x^(-1/2). Usually I would then set the derivative equal to zero, but there really isn't anything you can do to solve it. So I'm wondering if the answer would be none? I'm not sure what to do. If you could help that would be great.

Answer
Questioner:    Alexis
Private: No
Question: Find all the points at which the tangent line to the curve is horizontal.

f(x) = square root of x

I rewrote the function as (x)^1/2 and then found the derivative, which was 1/2x^(-1/2). Usually I would then set the derivative equal to zero, but there really isn't anything you can do to solve it. So I'm wondering if the answer would be none? I'm not sure what to do. If you could help that would be great.
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You are correct.  There are no stationary points, where f'(x) = 0.  So no horizontal tangents.