Question

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

Answer 1

are you allowed to take the derivative?

Answer 2

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

Answer 3

let me try that real quick

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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