Science:Math Exam Resources/Courses/MATH102/December 2019/Question 05 (a)/Solution 1

The slope of the tangent line to the curve $y=f(x)$ is equal to $f^{\prime }(x)$.

$f^{\prime }(10)=\frac{1}{(1+10{)}^2}=\frac{1}{121}$. Using the slope-point form, the tangent line equation is

$y-\frac{10}{11}=\frac{1}{121}(x-10)$,

i.e.

$y=\frac{1}{121}x+\frac{100}{121}$.