Question

Find all points on the graph of the function f(x)=x^2/x+2 where the tangent line is horizonal.
I get to x^2+4x/(x+2)^2
Then I get to x=-4 and x=0.
Am I on the right path?

Answer 1

tangent line horizontal is a slope of 0, so when you have the derivative (which you have is correct) equalling 0, this is the answer. yes, you are correct.

Answer 2

Yes. The roots of x(x+4)=0 are 0 and -4 respectively

Answer 3

so i get one point as (-4,-8)
when I replace the 0 i get 0/2, so will this not be a point where the tangent line is horizonal?

Answer 4

Plug the solutions into f(x) one at a time to obtain the associated y coordinate.
The coordinates of the points of interest are (0,0) and (-4,-8 ).

Answer 5

http://www.coolmath.com/graphit/ provides an online graphing program.

Plot x^2/(x+2). The curve in the area of the origin, (0,0) is hardly curving, however, the tangent line at the point (0,0) seems to the casual observer to be parallel to the x axis, ie: horizontal. The other tangent line at (-4,-8) easier to verify.

Answer 6

Thanks