Problem
Fid the value of \( k \) such that the tangent line to the graph of \( f(x)=\frac{k+x}{x^{2}} \) has slop 5 at \( x=2 \)
Solution
Step 1 ：\( f'(x) = \frac{-2(k+x)}{x^{3}} \)
Step 2 ：\( f'(2) = \frac{-2(k+2)}{2^{3}} \)
Step 3 ：\( 5 = \frac{-2(k+2)}{8} \)
