Find all values of x if any where the tangent line to the graph of the given equation is horizontal?

Question

y= x - sqrt (x)

I am very confused would I work it like this?
y = x - x^-1/2 then set x = 0?

Please explain. thank you!

Answer 1

You have the right idea, but

y' = 1 - 1/(2√x)

Setting that to zero, we get

1 - 1/(2√x) = 0
1/(2√x) = 1
2√x = 1
√x = 1/2
x = 1/4

As you can see from the graph, there is only the one point (1/4,-1/4) with a horizontal tangent.

http://www.wolframalpha.com/input/?i=x-%E2%88%9Ax