Question

find the x coordinate of the point where the graph of the function

f(x)=x(sqrt(1-3x))

has a horizontal tanget line

Answer 1

It has a horizontal tangent line when the point in the curve is a stationary point.

So go ahead to differentiate f(x)

f(x)=x(sqrt(1-3x))
\[\frac{df(x)}{dx}= \frac{2-9x}{2\sqrt{1-3x}}\]

Let df(x)/dx = 0 to find the value of x that is equals to the stationary point.

0= (2-9x)/ (2srt(1-3x)) [since denominator cannot be equals to 0]
2-9x= 0
x= 2/9

Answer 2

where did you get the numerator?

Answer 3

It is because of the differentiation.

Answer 4

how does that differentiate to get what you got for df(x)/dx=???

Answer 5

http://www.wolframalpha.com/input/?i=+x%28sqrt%281-3x%29%29

Go the part at differentiation and click show steps.