find an equation for line tangent to the curve when x=2 f(x)=8/x

Question

find an equation for line tangent to the curve when x=2     f(x)=8/x

anonymous · Answer

are you allowed to take the derivative?

anonymous · Answer

if so then the derivative of $f(x)=\frac{8}{x}$ is $f'(x)=-\frac{8}{x^2}$ 
find $f'(2)$ and then use the point-slope formula

anonymous · Answer

let me try that real quick

anonymous · Answer

the equation I get is: y=2x but i don't believe that is correct..not sure though?

anonymous · Answer

no it is not correct because $f(2)=-\frac{8}{2^2}=-2$ for one thing

anonymous · Answer

and $f(2)=4$ so your have a slope of $-2$ and a point of $(2,4)$ the point slope formula will give you the answer

anonymous · Answer

ok so then i use the point slope formula and i get: y-4=-2(x-2) then i distribute and get: y-4=-2x+4 then add for and get the final answer y=-2x+8...do you agree