Find all $x$ values such that the tangent line to the given curve satisfy a specific property.
(a) $y=\frac{x²+1}{x+2}$; horizontal. (Answer = $-2
+\sqrt3$)(b)$y=\frac{x²+1}{x+1}$; parallel to $y=x$. (Answer = none)
The tangent problem is confusing me a bit. Could anybody walk me through the steps I need to solve this problem? Thanks in advance.
Best Answer
Hint: For a) $$f'(x)=\frac{x^2+2x-1}{(1+x)^2}$$ so it must be $$f'(x)=0$$ For b) such Tangent line must have the form
$y=x+n$ so solve the equation $$x+n=\frac{x^2+1}{x+1}$$ and set the discriminante equal to Zero.