How do you find the points on the tangent line?

[Guest]

The question is: Find the point(s) at which the tangent to the curve is horizontal.
a) y= 2x^2/(x-4) I think that you make y=0 so that means the tangent is horizontal, however, what do you do next to find the points?
The ans to this question is (0,0) and (8,32)

Also next question: Show that there are no tangents to the graph of f(x)=(5x+2)/(x+2) that have a negative slope.

Once again, thanks so much for the help and time

 

[stapel]

I think that you make y=0 so that means the tangent is horizontal...

No. It should have been mentioned in class that the slope of the tangent line is zero where the derivative is zero, not where the original function crosses the x-axis (where "y = 0").

Show that there are no tangents to the graph of f(x)=(5x+2)/(x+2) that have a negative slope.

Take the derivative, and show that it is never negative.

Eliz.