Объяснение:

[tex]f(x)=\frac{5}{x} \ \ \ \ \ x_0=7\ \ \ \ y_k=?\\y_k(x_0)=y(x_0)+y'(x_0)*(x-x_0)\\y(x_0)=\frac{5}{7} .\\y'(x_0)=(\frac{5}{x})' =\frac{5'*x*5*x'}{x^2}=\frac{0*x-5*1}{x^2}=-\frac{5}{x^2} .\\ y'(7)=-\frac{5}{7^2}=-\frac{5}{49}.\\y_k= \frac{5}{7}-\frac{5}{49}*(x-7)=\frac{5}{7} -\frac{5}{49} x+\frac{5}{7}=-\frac{5}{49}x+\frac{10}{7}=\frac{10}{7}-\frac{5}{49}x .[/tex]

[tex]OTBET:\ y_k=\frac{10}{7} -\frac{5}{49}x.[/tex]