@satellite73 okay so the questions is "find all points x,y on the curve where the line tangent to the curve has slope -1/2. so the curve given is y=(2x-5)/(x^2-4) and the derivative was [-2(x-4)(x-1)]/[(x^2-4)^2]

Question

anonymous · Answer

ah in that case, set the derivative equal to -1/2 and solve for x

anonymous · Answer

yeah thats the hard part. I don't know how. I tried doing it by calculator thru intersection but it wouldnt work

anonymous · Answer

ok we can do that part

anonymous · Answer

okay so we have 2(x-4)(x-1)]/[(x^2-4)^2=-1/2

anonymous · Answer

i think you might be off by a minus sign.  let me check carefully. 
$$\frac{-2(x-4)(x-1)}{(x^2-4)^2}=-\frac{1}{2}$$

anonymous · Answer

oh no you have it on the first line. ok

anonymous · Answer

so the first step would be to get rid of the denominator right?

anonymous · Answer

this means 
$$\frac{2(x-4)(x-1)}{(x^2-4)^2}=\frac{1}{2}$$ so 
$$4(x-4)(x-1)=(x^2-4)^2$$

anonymous · Answer

now that i have started i have no clue as to how you are supposed to continue because you have a polynomial of degree 4

anonymous · Answer

i got this from wolfram http://www.wolframalpha.com/input/?i=4%28x-4%29%28x-1%29%3D%28x%5E2-4%29%5E2 two real solutions, but how you are supposed to get the second one i have absolutely no idea

anonymous · Answer

well thanks anyway. I'll just ask one of the math teachers tomorrow early morning.

anonymous · Answer

i checked and your derivative is correct. maybe they gave you this problem without thinking it through