y=x^2/x+1 find all x values at which the tangent line is parallel to the line y=x
after you find the quotient of the problem how do you determine if its parallel to y=x
im at x^2+2x-1/x^2+2x+1
It changes things a little:
$\displaystyle \frac{\,dy}{\,dx}=\frac{2x(x+1)-(x^2+1)}{(x+1)^2}=\frac{x^2+2x-1}{(x+1)^2}$
Find the value of x that causes $\displaystyle \frac{\,dy}{\,dx}=1$
This implies that $\displaystyle \frac{x^2+2x-1}{(x+1)^2}=1\implies x^2+2x-1=x^2+2x+1$
Can this ever be true?
--Chris