Find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate.
f(x) = x + 2/x; x = 2

Question

Find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate.
f(x) = x + 2/x;  x = 2

anonymous · Answer

$$f(x)=\frac{x+2}{x}$$
$$f'(x)=\frac{-2}{x^2}$$ 
$$f'(2)=-\frac{1}{2}$$ is your slope, and your point is 
$$(2,2)$$ and point slope formula give the answer

anonymous · Answer

Wait let me rewrite that equation.

anonymous · Answer

f(x) = x + (2/x);  x = 2

anonymous · Answer

well... same idea, different answer

anonymous · Answer

My answer was y=-x+5 but it was incorrect.

anonymous · Answer

f prime of x = 1 + (-2/x^2) right?

anonymous · Answer

$$f'(x)=1-\frac{2}{x^2}$$ 
$$f'(2)=1-\frac{1}{2}=\frac{1}{2}$$ now use point slope with 
$$(2,3)$$

anonymous · Answer

Oh I see. I plugged in one instead of 2.

anonymous · Answer

.5x+4?