Question

find all values of x at which the tangent line is horizontal at y=(x^2-1)/(x+2)

Answer 1

Dannibe7, do you know what a horizontal tangent line is?

Answer 2

where the slope of the tan line is zero?

Answer 3

I presume you know how to differentiate?

Answer 4

i got that the derivative is (x^2+4x+1)/(x+2)^2 but what do i do to find where it is horizontal?

Answer 5

By definition, the derivative of a function is the slope of the tangent line at any point on this function. When is a slope horizontal?

Answer 6

when it is zero. but i dont know how to get it to that point after i find the derivative

Answer 7

That's correct!\[f(x)=\frac{x^2-1}{x+2}\]\[f'(x)=\frac{x^2+4x+1}{(x+2)^2}\]Now, since we know the slope has to be zero, all we have to do is solve the following equation:\[\frac{x^2+4x+1}{(x+2)^2}=0.\]Am I correct?

Answer 8

thats what I thought to do but i cant come up with the right answer
the answer is supposed to be \[-2\pm \sqrt{3}\]

Answer 9

correct ans

Answer 10

\[\frac{x^2+4x+1}{(x+2)^2}=0,\]\[x^2+4x=-1,\]\[x^2+4x+4=-1+4,\]in that step above, I simply completed the squares,\[(x+2)^2=3,\]\[x+2=\pm\sqrt{3}\]\[x=-2\pm\sqrt{3}.\]All I did was algebra.

Answer 11

what is completing the square?

Answer 12

Since there are sources that can do a better job than me at explaining what it is, I will link you to this website:

http://www.purplemath.com/modules/sqrquad.htm