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 $\displaystyle \frac{2}{x}$ is $\displaystyle -\frac{2}{x^2}$. Plug in $\displaystyle x=7$ to get that $\displaystyle m=-\frac{2}{49}$.

Spoiler:
Use point slope form for the equation:

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

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 $\displaystyle \left(7 , \frac{2}{7} \right)$

$\displaystyle y = 2x^{-1}$

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

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

now finish.