Answer:
[tex]y=-\frac{1}{5} x+2[/tex]
Step-by-step explanation:
f(x) = [tex]\frac{5}{x}[/tex] ⇒ f(x) = [tex]5x^{-1[/tex]
Use the power rule to diferentiate:
f'(x) = [tex]-5x^{-2[/tex]
Plug in the value to differentiate at:
f'(5) = [tex]-5(5)^{-2[/tex] = [tex]-\frac{1}{5}[/tex] = [tex]m[/tex]
Plug into the equation of the tangent line:
[tex]y-f(5)=f'(5)(x-5)[/tex]
[tex]y=f'(5)(x-5)+f(5)[/tex]
[tex]y=-\frac{1}{5} (x-5)+1[/tex]
[tex]y=-\frac{1}{5} x+2[/tex]
