1. ## tangent line

The slope of the tangent line to the curve at the point is: i got 0.040816326 but its wrong

The equation of this tangent line can be written in the form where is:

and where is:

2. Originally Posted by wannous
The slope of the tangent line to the curve at the point is: i got 0.040816326 but its wrong

The equation of this tangent line can be written in the form where is:

and where is:
Your answer is wrong because you forgot the minus sign. The derivative of $\frac{2}{x}$ is $-\frac{2}{x^2}$. Plug in $x=7$ to get that $m=-\frac{2}{49}$.

Spoiler:
Use point slope form for the equation:

$y-\frac{2}{7}=-\frac{2}{49}(x-7) \implies y=-\frac{2}{49}x+\frac{4}{7}$

3. Originally Posted by wannous
The slope of the tangent line to the curve at the point is: i got 0.040816326 but its wrong

The equation of this tangent line can be written in the form where is:

and where is:
put away the calculator.

the point of tangency is $\left(7 , \frac{2}{7} \right)$

$y = 2x^{-1}$

$y' = -2x^{-2} = -\frac{2}{x^2}$

slope $= y'(7) = -\frac{2}{7^2} = -\frac{2}{49}
$

now finish.