Determine equation of tangent line of the function f(x)=e^2x/x^2 at x=1

Question

anonymous · Answer

$$
f'(x)=\frac{2 e^{2 x}
   (x-1)}{x^3}\
f(1)=0

$$
So the tangent is paralllel to the x-axis and  $f(1)=e^2$
So the the equation of the tangent is $ y=e^2$

anonymous · Answer

Se the graph around x=1 http://www.wolframalpha.com/input/?i=plot+e%5E%282x%29%2Fx%5E2+from+x%3D.5+to+x+%3D2

anonymous · Answer

See the graph with the tangent http://www.wolframalpha.com/input/?i=plot+%28e%5E2%2Ce%5E%282x%29%2Fx%5E2+%29from+x%3D.5+to+x+%3D2

anonymous · Answer

sorry, in my post above f'(1)=0

anonymous · Answer

we have to derivate this funcion, with the chain rule and quotient rule

$$f'(x)=\frac{2xe^{2x}*(x-1)}{x^4}$$

$$f'(x)=\frac{2e^{2x}*(x-1)}{x^3}$$

$$f'(1)=\frac{2e^{2}*(1-1)}{1^3}$$

$$\boxed{\boxed{f'(1)=0}}$$