**Step 1:** We utilize the regulations of backers to create the feature with only mathematical backers as well as hence compute its acquired:

$ latex f( x)= x ^ 3 +8 x ^ {-1} $

$ latex f'( x)= x ^ 2-8x ^ {-2} $

$ latex f'( x)= x ^ 2-frac {8} {x ^ 2} $

**Step 2:** The incline of the tangent at (2, 4) is discovered by assessing $latex f'( 2 )$:

$ latex m _ {1} =f'( 2 )=( 2 )^ 2-frac {8} {2 ^ 2} $

$ latex =4-2$

$ latex m _ {1} =2$

**Step 3:** We utilize the incline from action 2 to figure out the incline of the typical as well as we have $latex m=- frac {1} {2} $.

** Step 4:** Utilizing the incline from action 3, we have the formula $latex y=- frac {1} {2} x+ b$. Currently, we utilize the factor (2, -2) in the formula to locate the worth of

*b*:

$ latex y=- frac {1} {2} x+ b$

$ latex -2=- frac {1} {2} (2 )+ b$

$ latex b= -1$

**Step 5:** The formula of the typical line at the factor (2, 4) is $latex y=- frac {1} {2} x-1$.